Question

1. A 200.0 g mass vibrates in Simple Harmonic Motion with a total energy of 24.7 J and a frequency of 5.0 Hz.
(a) Find the spring constant k
(b) Find the maximum displacement
(c) Find the position, velocity and acceleration as a function of time.

Answer 1

a)

$$2\pi f=\sqrt{\frac{k}{m}}$$

$$2\pi (5)=\sqrt{\frac{k}{0.2}}$$

$$k=197 \frac{N}{m}$$

b)

$$E=0.5kA^2$$

$$A=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(24.7)}{197}}=0.500\ m$$

c)

$$x=A\sin{(2\pi ft)}=0.5\sin{(10\pi t)}$$

$$v=0.5(10\pi)\sin{(10\pi t)}=5\pi \sin{(10\pi t)}$$

$$a=-0.5(10\pi)^2\sin{(10\pi t)}=-50\pi^2\sin{(10\pi t)}$$