Question

a body of mass 30g suspended from the end of a
spiral spring whose force constant is 0.5 N/M. the body
is set into harmonic motion with amplitude 0.4m
calculate;
A. the period of the motion T
B. the frequency of the motion
C. the angular speed
D. the total energy

Answer 1

a.

$$T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{0.03}{0.5}}=1.54\ s.$$

b.

$$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}=\frac{1}{2\pi}\sqrt{\frac{0.5}{0.03}}=0.65\ Hz$$

c.

$$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{0.5}{0.03}}=4.08\frac{rad}{s}$$

d.

$$E=0.5kA^2=0.5(0.5)(0.4)^2=0.04\ J$$