Question

A particle with a mass of 9.00 ✕ 10-20 kg is vibrating with simple harmonic motion with a period of 3.00 ✕ 10-5 s and a maximum speed of 7.00 ✕ 103 m/s. (a) Calculate the angular frequency of the particle. rad/s (b) Calculate the maximum displacement of the particle.

Answer 1

Answer:

(a) $\omega=2.09*10^{5}\frac{rad}{s}$

(b) $A_{max}=0.033m$

Explanation:

(a) The angular frequency is defined as:

$\omega=2\pi f$

Here f is the frequency of the particle, which is inversely proportional to its period:

$f=\frac{1}{T}$

Replacing, we have:

$\omega=\frac{2\pi}{T}\\\omega=\frac{2\pi}{3*10^{-5}s}\\\omega=2.09*10^{5}\frac{rad}{s}$

(b) The maximum displacement is given by:

$A_{max}=\frac{v_{max}}{\omega}\\A_{max}=\frac{7*10^3\frac{m}{s}}{2.09*10^5\frac{rad}{s}}\\A_{max}=0.033m$