Energy in SHM: A 0.25 kg ideal harmonic oscillator has a total mechanical energy of If the oscillation amplitude is what is the oscillation frequency?
A) 4.5 Hz
B) 1.4 Hz
C) 2.3 Hz
D) 3.2 Hz

Question

Energy in SHM: A 0.25 kg ideal harmonic oscillator has a total mechanical energy of  If the oscillation amplitude is  what is the oscillation frequency?
A) 4.5 Hz 
B) 1.4 Hz 
C) 2.3 Hz 
D) 3.2 Hz

Quizplus · Accepted Answer

We can use the equation for the total mechanical energy of a spring-mass system:

$E = \frac{1}{2}kA^2$

where $k$ is the spring constant and $A$ is the amplitude. Since we know the total mechanical energy, we can solve for $k$:

$E = \frac{1}{2}kA^2$
$k = \frac{2E}{A^2}$

Next, we can use the equation for the frequency of a spring-mass system:

$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$

where $m$ is the mass. Plugging in the values we know, we get:

$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \frac{1}{2\pi}\sqrt{\frac{2E}{Am}}$

Plugging in the given values, we get:

$f = \frac{1}{2\pi}\sqrt{\frac{2(11	imes10^6)}{(0.25)(11)}}= 4.5$ Hz

Therefore, the correct answer is A.

Energy in SHM: a 0