Answer to Question #276932 in Classical Mechanics for gelo

Question

​1 kg block vibrates in shm with amplitude of 15 cm and period of T = 2 s find the frequency, its maximum speed and its speed

when the displacement is 5cm, its maximum acceleration when the displacement is 5cm.

 

Answer 1

Frequency:

$$f=\frac 1T=0.5\text{ Hz}.$$

Maximum speed:

$$v_\text{max}=2\pi fA=0.47\text{ m/s}.$$

Speed at x=5 cm:

$$x(t)=5=15\cos(2\pi ft),\\ t=0.39\text{ s},\\ v=-v_\text{max}\sin(2\pi ft)=0.44\text{ m/s}.$$

Acceleration when the displacement is 5 cm:

$$a=-(2\pi f)^2A\sin(2\pi ft)=-1.39\text{ m/s}^2.$$