Question

A 4kg panel of a car oscillators with frequency 5hz amplitude of 25cm . If the oscillation is assumed to be S.H.M calculate

The maximum velocity of the panel

The total energy of the panel

The maximum potential and K.E energy of the panel is 2cm from its equlibrium equation

Answer 1

Given:

$m=4\:\rm kg$

$f=5\rm\: Hz$

$A=0.25\:\rm m$

The maximum velocity of the panel

$$v_{\max}=A\omega=2\pi fA \\=2*3.14*5*0.25=7.85\:\rm m/s$$

The total energy of the panel

$$W=\frac{m\omega^2A^2}{2}=\frac{4\pi^2mf^2A^2}{2}$$

$$=\frac{4*3.14^2*4*5^2*0.25^2}{2}=123\:\rm J$$

The maximum potential and K.E energy of the panel

$$E_{k\max}=E_{p\max}=W=123\:\rm J$$