Question 1

A particle is moving with SHM.If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position,then calculate its period of oscillation.
A)5.4 s
B)6.4 s
C)7.4 s
D)10.8 s
E)none of the above

Accepted Answer

The answer of A particle is moving with SHM.If it...

Question 2

When the compression of a spring is doubled,the potential energy stored in the spring is
A)the same as before.
B)doubled.
C)tripled.
D)increased by a factor of 8.
E)None of these is correct.

Accepted Answer

The potential energy stored in a spring is proportional to the square of its compression (or extension). If the compression is doubled, the potential energy increases by a factor of 4, not 8.

Question 3

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface. 
-What is the rotational kinetic energy when the sphere is at the equilibrium position?
A) 
B) 
C) 
D) 
E)undetermined

Accepted Answer

The answer of Use the figure to answer the next...

Question 4

A simple way to test if a device can withstand high "g-force" is to attach the device to a vibrating platform.Suppose a device has to withstand up to 5g's,and the amplitude of the oscillation is 5 cm,the frequency of the vibration should be
A)5 Hz
B)981 Hz
C)31.3 Hz
D)44.3 Hz
E)62.6 Hz

Accepted Answer

The answer of A simple way to test if a...

Question 5

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m.The spring is stretched 10 cm from equilibrium and released.What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?
A)5.6 J
B)11 J
C)17 J
D)14 J
E)42 J

Accepted Answer

The answer of A 2.5-kg object is attached to a...

Question 6

The displacement in simple harmonic motion is a maximum when the
A)acceleration is zero.
B)velocity is a maximum.
C)velocity is zero.
D)kinetic energy is a maximum.
E)potential energy is a minimum.

Accepted Answer

In simple harmonic motion, the displacement is at its maximum when the object is at its furthest point from the equilibrium position, which is also when its velocity is zero because it momentarily stops before changing direction.

Question 7

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of
A)0.7
B)1.0
C)1.4
D)2.0
E)4.0

Accepted Answer

The energy of a simple harmonic oscillator is proportional to the square of its amplitude (E ∝ A^2). To double the energy, the amplitude must be increased by a factor of the square root of 2, which is approximately 1.4.

Question 8

A system consists of a mass vibrating on the end of a spring.The total mechanical energy of this system
A)varies as a sine or cosine function.
B)is constant only when the mass is at maximum displacement.
C)is a maximum when the mass is at its equilibrium position only.
D)is constant,regardless of the displacement of the mass from the equilibrium position.
E)is always equal to the square of the amplitude.

Accepted Answer

The total mechanical energy of a simple harmonic motion system (such as a mass on a spring) remains constant, regardless of the displacement of the mass from the equilibrium position. This is due to the conservation of mechanical energy in a system with no external forces acting on it. The energy oscillates between kinetic and potential energy, but the total amount of energy remains constant.

Question 9

When the displacement of an object in simple harmonic motion is one-quarter of the amplitude A,the potential energy is what fraction of the total energy?
A) 
B) 
C)1/16
D)There is not enough information provided to answer correctly
E)None of these is correct.

Accepted Answer

The answer of When the displacement of an object in...

Question 10

The force constant for a simple harmonic motion is k and the amplitude of the motion is A.The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is A) B) kA² C)kA² D)kA E)None of these is correct.

Accepted Answer

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Question 11

If the amplitude of a simple harmonic oscillator is doubled,the total energy is
A)unchanged.
B)one-fourth as large.
C)half as large.
D)doubled.
E)quadrupled.

Accepted Answer

The amplitude of a simple harmonic oscillator is directly proportional to its total energy. Therefore, if the amplitude is doubled, the total energy is quadrupled (2² = 4). Hence, the correct option is E.

Question 12

In simple harmonic motion,the magnitude of the acceleration of a body is always directly proportional to its
A)displacement.
B)velocity.
C)mass.
D)potential energy.
E)kinetic energy.

Accepted Answer

The answer of In simple harmonic motion,the magnitude of the...

Question 13

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface. 
-The angular frequency of the oscillation is
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the figure to answer the next...

Question 14

The displacement of a body moving with simple harmonic motion is given by the equation  After one-quarter of a period has elapsed since t = 0,which of the following statements is correct?
A)Half the total energy of the body is kinetic energy and half is potential energy.
B)The kinetic energy is a maximum.
C)The potential energy is a maximum.
D)The total energy is a negative maximum.
E)Both kinetic and potential energies are maxima.

Accepted Answer

The answer of The displacement of a body moving with...

Question 15

A 2.50-kg object is attached to a spring of force constant k = 4.50 kN/m.The spring is stretched 10.0 cm from equilibrium and released.What is the maximum kinetic energy of this system? A)45.0 J B)22.5 J C)56.0 J D)2.25 $\times$ 10⁵ J E)4.50 J

Accepted Answer

The answer of A 2.50-kg object is attached to a...

Question 16

A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm.When the mass is 2.0 cm from the equilibrium position,what fraction of its total energy is potential energy?
A)one-quarter
B)one-third
C)one-half
D)two-thirds
E)three-quarters

Accepted Answer

The answer of A mass attached to a spring has...

Question 17

Which of the following statements is true of a particle that is moving in simple harmonic motion?
A)The momentum of the particle is constant.
B)The kinetic energy of the particle is constant.
C)The potential energy of Earth-particle system is constant.
D)The acceleration of the particle is constant.
E)The force the particle experiences is a negative restoring force.

Accepted Answer

In simple harmonic motion, the force acting on the particle is a restoring force that is always directed towards the equilibrium position and is proportional to the displacement from that position. This force is negative because it acts in the opposite direction of the displacement, aiming to restore the particle to its equilibrium position. The other options are incorrect because in simple harmonic motion, the momentum, kinetic energy, potential energy, and acceleration of the particle are not constant; they vary as the particle oscillates.

Question 18

A body moving in simple harmonic motion has maximum acceleration when it has
A)maximum velocity.
B)maximum kinetic energy.
C)minimum potential energy.
D)minimum kinetic energy.
E)zero displacement.

Accepted Answer

In simple harmonic motion, maximum acceleration occurs at maximum displacement, where kinetic energy is minimum.

Question 19

A mass on a spring oscillates with an amplitude of 5.0 cm.What is the position of the mass when the kinetic and potential energies are equal?
A)There is not enough information provided to answer this question.
B)1.2 cm
C)2.5 cm
D)3.5 cm
E)3.8 cm

Accepted Answer

The kinetic and potential energies are equal at a position where the displacement is $\sqrt{1/2}$ of the amplitude. Given an amplitude of 5.0 cm, the position is $5.0 \times \sqrt{1/2} = 5.0 \times 0.707 \approx 3.5$ cm.

Question 20

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface. 
-What is the linear kinetic energy when the sphere is at the equilibrium position?
A) 
B) 
C) 
D) 
E)undetermined

Accepted Answer

At the equilibrium position, the spring is at its natural length and the sphere is at rest. Therefore, all of the initial potential energy stored in the spring is converted to kinetic energy. The potential energy stored in the spring is given by U = 0.5kA^2. 
The total energy of the system is conserved, so at the equilibrium position, all of this potential energy is converted to the linear kinetic energy of the center of mass of the sphere: 
0.5kA^2 = 0.5mv^2 
v^2 = kA^2/m 
The linear kinetic energy of the center of mass is given by K = 0.5mv^2 = 0.5kA^2. Substituting the given values, we have K = 0.5(2/5mr^2)(A^2/r^2) = 1/5mA^2. Therefore, choice B is correct.

Quiz 14: Oscillations

A particle is moving with SHM.If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position,then calculate its period of oscillation.

When the compression of a spring is doubled,the potential energy stored in the spring is

A simple way to test if a device can withstand high "g-force" is to attach the device to a vibrating platform.Suppose a device has to withstand up to 5g's,and the amplitude of the oscillation is 5 cm,the frequency of the vibration should be

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m.The spring is stretched 10 cm from equilibrium and released.What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?

The displacement in simple harmonic motion is a maximum when the

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of

A system consists of a mass vibrating on the end of a spring.The total mechanical energy of this system

When the displacement of an object in simple harmonic motion is one-quarter of the amplitude A,the potential energy is what fraction of the total energy?

The force constant for a simple harmonic motion is k and the amplitude of the motion is A.The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is

If the amplitude of a simple harmonic oscillator is doubled,the total energy is

In simple harmonic motion,the magnitude of the acceleration of a body is always directly proportional to its

The displacement of a body moving with simple harmonic motion is given by the equation After one-quarter of a period has elapsed since t = 0,which of the following statements is correct?

A 2.50-kg object is attached to a spring of force constant k = 4.50 kN/m.The spring is stretched 10.0 cm from equilibrium and released.What is the maximum kinetic energy of this system?

A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm.When the mass is 2.0 cm from the equilibrium position,what fraction of its total energy is potential energy?

Which of the following statements is true of a particle that is moving in simple harmonic motion?

A body moving in simple harmonic motion has maximum acceleration when it has

A mass on a spring oscillates with an amplitude of 5.0 cm.What is the position of the mass when the kinetic and potential energies are equal?