Question

A spring with a cart at its end vibrates at frequency 8.5Hz.
1.Determine the period of vibration
2.Determine the frequency if the cart's mass is doubled while the spring constant remains unchanged.
3.Determine the frequency if the spring constant doubles while the cart's mass remains the same.

Answer 1

F = -kx = m a
assume simple harmonic motion
y = A sin (2 pi f t)
then
a = acceleration = - (2 pi f)^2 y
ans
-k y = - m (2 pi f)^2 y
or
2 pi f = sqrt (k/m)
period = 1/f = (1/2pi) sqrt(m/k)

double m
2 pi f' = sqrt(k/2m) = old f/sqrt 2

3. well same deal but times sqrt 2 now