# Problem: A spring with a cart at its end vibrates at frequency 5.0 Hz.A. Determine the period of vibration.B. Determine the frequency if the cart's mass is doubled while the spring constant remains unchanged.C. Determine the frequency if the spring constant doubles while the cart's mass remains the same.

###### FREE Expert Solution

We need to remember the following equations to smoothly solve this problem

Period of vibration:

$\overline{){\mathbf{T}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{f}}}$, where f is linear frequency.

Angular frequency:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\sqrt{\frac{\mathbf{k}}{\mathbf{m}}}}$, where k is spring constant and m is mass.

A.

From the equation for the period, we have:

86% (230 ratings) ###### Problem Details

A spring with a cart at its end vibrates at frequency 5.0 Hz.
A. Determine the period of vibration.
B. Determine the frequency if the cart's mass is doubled while the spring constant remains unchanged.
C. Determine the frequency if the spring constant doubles while the cart's mass remains the same.