CAIE A-Level Physics 17.2.2 Total Energy in SHM

Practise using E = 1/2 m omega² x0² to calculate total SHM energy or recover mass, frequency or amplitude, and relate energy to motion.

Exam points

calculate total SHM energy using E = 1/2mω²x₀²
rearrange the expression to determine mass, angular frequency or amplitude
relate total energy to the kinetic and potential-energy distribution during the motion

[Maximum number: 3]

A small wooden block (cuboid) of mass m floats in water, as shown in Fig. 3.1.

Fig. 3.1

The top face of the block is horizontal and has area A. The density of the water is $\rho$ .

The block is now placed in a liquid with a greater density. The block is displaced and released so that it oscillates vertically. The variation with displacement x of the acceleration a of the block is measured for the first half oscillation, as shown in Fig. 3.3.

Fig. 3.3

The mass of the block is 0.57 kg .

Use Fig. 3.3 to determine the decrease $\Delta E$ in energy of the oscillation for the first half oscillation.
E= J

$(E=) 1 / 2 m \omega^{2} x_{0}{ }^{2}$

C1

$\omega^{2}=(-)$ gradient

C1

$\begin{aligned} (E=) 1 / 2 m \omega^{2}\left(x_{1}^{2}-x_{2}^{2}\right) =1 / 2 \times 0.57 \times(2.3 / 0.020)\left(0.020^{2}-0.016^{2}\right) =4.7 \times 10^{-3} \mathrm{~J} \end{aligned}$

A1

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17.2.2—E = 1/2 mω2x0 2 for the total energy of a system undergoing simple harmonic question 1