The system has maximum kinetic energy when the displacement is zero because the oscillator is at its equilibrium position and so moving at maximum velocity.
The total energy of a simple harmonic system always remains constant and is equal to the sum of the kinetic and potential energies
The kinetic and potential energy of an oscillator in SHM vary periodically
Potential and kinetic energy v displacement in half a period of an SHM oscillation
You may be expected to draw as well as interpret energy graphs against time or displacement in exam questions. Make sure the sketches of the curves are as even as possible and use a ruler to draw straight lines, for example, to represent the total energy.
The total energy of system undergoing simple harmonic motion is defined by:
A ball of mass 23 g is held between two fixed points A and B by two stretch helical springs, as shown in the figure below
The ball oscillates along the line AB with simple harmonic motion of frequency 4.8 Hz and amplitude 1.5 cm.Calculate the total energy of the oscillations.
Step 1: Write down all known quantities
Mass, m = 23 g = 23 × 10–3 kg
Amplitude, x0 = 1.5 cm = 0.015 m
Frequency, f = 4.8 Hz
Step 2: Write down the equation for the total energy of SHM oscillations:
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