A simple harmonic oscillator has amplitude 15 cm and it completes 100

Question

A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is $\pi$ /2, write expressions for its displacement and velocity. (iii) Calculate the values of maximum velocity and acceleration.

30 May 2025

Answer :

Word Count : 321

We are given: * Amplitude $A = 15\ \text{cm} = 0.15\ \text{m}$ * Number of oscillations $= 100$ in $t = 50\ \text{s}$ * Initial phase $\phi = \frac{\pi}{2}$ We are to solve manually. --- ### Step 1: Calculate Time Period and Angular Frequency Number of oscillations $n = 100$ in time $T_{\text{total}} = 50\ \text{s}$ $$ f = \frac{n}{T_{\text{total}}} = \frac{100}{50} = 2\ __________ ________ _________ __________ ___ ____ _______ ________ ____ ____.
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