Energy in simple harmonic motion

An object of mass $80\text{ g}$ carries out simple harmonic motion. The displacement $x$ of the object against time $t$ is illustrated in Fig. 4.1.

Feb/March 2016

A small object with mass $24\,\text{g}$ is resting on a platform. The platform is connected to an oscillator, as shown in Fig. 3.1, and the oscillator makes the platform move vertically up and down.

Feb/March 2024

As illustrated in Fig. 4.1, a small metal ball hangs from a fixed point on a string. It is displaced slightly sideways and then released. Fig. 4.2 shows how the ball’s horizontal displacement x changes with time t. The ball moves with simple harmonic motion.

May/June 2012

A ball with mass $37\,\text{g}$ is trapped between fixed points A and B by two stretched helical springs, as illustrated in Fig. 2.1. It moves to and fro along AB in simple harmonic motion with frequency $3.5\,\text{Hz}$ and amplitude $2.8\,\text{cm}$.

May/June 2012

A small metal ball hangs from a fixed point on a string, as in Fig. 4.1. It is displaced a short distance sideways and then let go. Figure 4.2 shows how the horizontal displacement $x$ changes with time $t$. The ball moves with simple harmonic motion.

May/June 2012

A spring hangs a mass of $78\,\text{g}$ from a fixed point, as shown in Fig. 3.1. The mass at rest is moved vertically downward by $2.1\,\text{cm}$ and then let go. It is seen to execute simple harmonic motion with a period of $0.69\,\text{s}$. The release occurs at time $t = 0$.

May/June 2013

A student examines the energy changes for a mass oscillating on a vertical spring, as shown in Fig. 4.1. The student sketches a graph showing how energy $E$ of the oscillation varies with displacement $x$, as shown in Fig. 4.2.

May/June 2014

A student studies how the energy of a mass moving up and down on a vertical spring changes, as illustrated in Fig. 4.1. The student then plots a graph of how energy $E$ varies with displacement $x$ for the oscillation, as shown in Fig. 4.2.

May/June 2014

State the meaning of simple harmonic motion.

May/June 2015

A small steel sphere is performing vertical oscillations at the end of a spring, as illustrated in Fig. 4.1. The sphere's velocity $v$ depends on its displacement $x$ from equilibrium as follows $v = \pm 9.7\sqrt{(11.6 - x^2)}$, where $v$ is in $\text{cm s}^{-1}$ and $x$ is in $\text{cm}$.

May/June 2023

A cuboidal block is floating in a liquid with its base horizontal, as illustrated in Fig. 5.1. The lower face of the block lies a depth $h$ beneath the liquid surface. The block is moved a small distance downward and then let go, causing it to oscillate. Fig. 5.2 gives the way the block’s acceleration $a$ changes with $h$. Fig. 5.3 gives the way the block’s kinetic energy $E_K$ changes with $h$.

May/June 2025

A cuboid-shaped block floats in a liquid with its base kept horizontal, as shown in Fig. 5.1. The base of the block lies at a depth $h$ beneath the liquid surface. The block is pushed down a small distance and then released, so it oscillates. Fig. 5.2 shows how the acceleration $a$ of the block varies with $h$. Fig. 5.3 shows how the kinetic energy $E_{K}$ of the block varies with $h$.

May/June 2025

What is meant by simple harmonic motion?

Oct/Nov 2011

As shown in Fig. 3.1, a metal ball hangs from a fixed point on a string. The ball is displaced by a small amount and then let go. Fig. 3.2 shows how the ball’s displacement $x$ changes with time $t$.

Oct/Nov 2013

As shown in Fig. 3.1, a metal ball hangs from a fixed point on a string. The ball is then given a slight displacement and released. Fig. 3.2 shows how the displacement $x$ of the ball changes with time $t$.

Oct/Nov 2013

A simple pendulum is made up of a metal sphere hanging from a fixed point by a thread, as shown in Fig. 3.1. The sphere has mass $94.0\,\text{g}$ and is pulled sideways by a horizontal distance of $12.7\,\text{cm}$. Its centre of gravity rises vertically by $0.90\,\text{cm}$. The sphere is then released, so it oscillates. The sphere may be taken to oscillate with simple harmonic motion.

Oct/Nov 2020

Fig. 4.1 illustrates how the height $h$ above the ground changes with time $t$ for an object of mass $36\,\text{kg}$ moving in vertical simple harmonic motion.

Oct/Nov 2022

Fig. 5.1 shows a pendulum made of a metal sphere hanging from a thin string. The sphere makes small oscillations around its equilibrium position. These oscillations can be treated as simple harmonic. Fig. 5.2 shows how the displacement $x$ of the sphere from equilibrium changes with time $t$.

Oct/Nov 2024