A mass of 0.40 kg,hanging from a spring with a spring constant of 160 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.
A) zero
B) 1.4 m/s
C) 1.7 m/s
D) 1.2 m/s

Question

Quizplus · Accepted Answer

The period of oscillation of a mass hanging from a spring can be calculated using:

T = 2π√(m/k)

where m is the mass of the object, k is the spring constant and T is the period of oscillation.

Using the given values, we get:

T = 2π√(0.40 kg/ 160 N/m) = 0.628 s

The speed of the mass at any point in its oscillation can be calculated using:

v = ωA

where A is the amplitude (maximum displacement) of the oscillation and ω is the angular frequency, given by:

ω = 2π/T

Using the given values, we have:

ω = 2π/0.628 s = 9.98 rad/s

A = 0.10 m (given)

So the speed of the mass when it is 0.05 m from its equilibrium position can be calculated as:

v = ωA = 9.98 rad/s x 0.05 m = 0.499 m/s

Therefore, the closest answer choice is C) 1.7 m/s.

A Mass of 0