Oscillations
Beginner
Simple harmonic oscillation
Source: Principles of Physics
Problem
An oscillating block-spring system takes 0.75 s to begin repeating its motion.
- Find the period.
- Find the frequency in hertz.
- Find the angular frequency in radians per second.
[Q1] T = 0.75 s [Q2] f = 1.3 Hz [Q3] \omega = 8.4 rad/s
[Q1] The period $T$ is the time required for the motion to complete one cycle. The problem states this time is 0.75 s.
[Q2] The frequency $f$ is the number of cycles per unit time, which is the reciprocal of the period.
$$f = \frac{1}{T}$$[Q3] The angular frequency $\omega$ is related to the period $T$ by the following equation:
$$\omega = \frac{2\pi}{T}$$Substituting the value $T = 0.75$ s into the equations for frequency and angular frequency:
$$f = \frac{1}{0.75 \text{ s}}$$ $$\omega = \frac{2\pi}{0.75 \text{ s}}$$