Question

A 2.00-kg object is attached to a spring. The force constant of the spring is k=196 N/m. The object is held a distance 5.00 cm from the equilibrium position and is released at t 0. (a) Find the angular frequency ω, (b) the frequency f, (c) the period T and (d) write x (in cm) as a function (cosine) of time.

Answer 1

(a)

$$\omega=\sqrt{\dfrac{k}{m}}=\sqrt{\dfrac{196\ \dfrac{N}{m}}{2\ kg}}=9.9\ \dfrac{rad}{s}.$$

(b)

$$\omega=2\pi f,$$ $$f=\dfrac{\omega}{2\pi}=\dfrac{9.9\ \dfrac{rad}{s}}{2\pi}=1.58\ Hz.$$

(c)

$$T=\dfrac{1}{f}=\dfrac{1}{1.58\ Hz}=0.63\ s.$$

(d) The position as a function of time can be written as follows:

$$x(t)=Acos(\omega t+\phi),$$

here, $A=5.0\ cm$, $\omega=9.9\ \dfrac{rad}{s}$ and $\phi=0$.

Finally, we get:

$$x=(5.0\ cm)cos[(9.9\ \dfrac{rad}{s})t].$$