Question

A spring of mass, m, oscillates with a frequency, f. Find an expression for the angular velocity, w. Also find the solution in form of x(t)

Answer 1

By definition, the angular velocity is:

$$\omega = 2\pi f$$

where $f$ is the frequency of the spring.

The solution is (simple harmonic motion):

$$x(t) = A\cos (\omega t + \phi)$$

where $A$ is the magnitude of the oscillations, $\omega$ is angular velocity, and $\phi$ is the initial phase shift.

Answer. 1) $\omega = 2\pi f$, 2) $x(t) = A\cos (\omega t + \phi)$.