Simple Harmonic Oscillation?

Question

A 2.00 kg executes simple harmonic oscillation w/ an amplitude of 5.00 cm. The max speed of the mass is 2.00 m/s.

a) determine the angular frequency of the oscillation

b) find the frequency of the oscillation

c) if the mass is at x = 0m when t = 0s, find x(t)

d) what is the position of the mass when t = 1.00s

Answer 1

(c)♦ x(t)= A*sin(w*t), where A=5cm =0.05m;

(a)♥ v(t) = x’(t) = A*w*cos(w*t), where A*w=2m/s, hence w=2/0.05 = 40rad/s;

(c)♦ x(t) = 0.05*sin(40*t);

(d)♠ x(1s) = 0.05*sin(40*1) =0.03726m = 3.726cm;

(b)♣ f=w/(2pi) = 6.366Hz;