K A Tsokos Solutions for Chapter: Wave Phenomena (HL), Exercise 1: Test yourself

Explain why the oscillations of a pendulum are, in general, not simple harmonic. State the condition that must be satisfied for the oscillations to become approximately simple harmonic.

Write down an equation for the displacement of a particle undergoing SHM with an amplitude equal to $8.0 \mathrm{cm}$ and a frequency of $14 \mathrm{Hz}$, assuming that at $t = 0 \mathrm{s}$ the displacement is $8.0 \mathrm{cm}$ and the particle is at rest.

Find the displacement, velocity and acceleration of this particle at a time of $0.025 \mathrm{s}$.

( The particle undergoing SHM with an amplitude equal to $8.0 \mathrm{cm}$ and a frequency of $14 \mathrm{Hz}$, assuming that at $t = 0 \mathrm{s}$ the displacement is $8.0 \mathrm{cm}$ and the particle is at rest.)

A point on a guitar string oscillates in SHM with an amplitude of $5.0 \mathrm{mm}$ and a frequency of $460 \mathrm{Hz}$. Determine the maximum velocity and acceleration of this point.

The graph shows the variation with time $t$ of the displacement $v$ of a particle executing SHM.

Draw a graph to show the variation with displacement $x$ of the acceleration $a$ of the particle (put numbers on the axes).