Block-Spring Oscillator Period and Frequency

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Oscillations Beginner Simple harmonic oscillation

Source: Principles of Physics

Problem

An oscillating block-spring system takes 0.75 s to begin repeating its motion.

  1. Find the period.
  2. Find the frequency in hertz.
  3. 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:

$$f = \frac{1}{0.75 \text{ s}}$$ $$\omega = \frac{2\pi}{0.75 \text{ s}}$$