Answer to Question #301097 in Physics for ccy

Question

A mass is hung at the end of the spring length of 14 cm. The mass was pull down

and extend to the quarter of the original length of the springs and released so that

it oscillates vertically. If the mass took 0.125 s to go up and down from

equilibrium point:

a) The acceleration when the displacement is at maximum.

Answer 1

Given:

$l_0=0.14\:\rm m$

$A=1/4l_0=0.035\:\rm m$

$T=0.125\:\rm s$

The angular frequency of oscillations

$$\omega=\frac{2\pi}{T}=\frac{2\pi}{0.125}=50.24\;\rm rad/s$$

The maximum acceleration

$$a_{\max}=A\omega^2\\ =0.035*50.24^2=88\:\rm m/s^2$$