Edexcel A-Level Physics A2 5.5.144 Shm Displacement Velocity and Acceleration Equations Questions

Practise Edexcel A-Level Physics SHM equations by using displacement, velocity and acceleration relationships with angular frequency.

Exam points

calculate maximum velocity or amplitude using vmax = Aω with ω = 2πf or 2π/T
use a = -ω²x to find acceleration, angular frequency or period from SHM data
match displacement, velocity and acceleration graphs using gradient and phase relationships

[Maximum number: 2]

A student added small lead spheres to a test tube. The student placed the test tube in a small beaker of water. The test tube floated as shown.

Figure for Question Edexcel A-Level Physics A2 5.5.144 Shm Displacement Velocity and Acceleration Equations Questions question 1 — Edexcel A-Level Physics A2

The student gave the test tube a small vertical displacement. The test tube then oscillated vertically.

The student replaced the water with another liquid. The period is given by $T=\sqrt{\frac{16\pi m}{D^2\rho g}},$ where D is the test-tube diameter, m is the mass of the test tube and spheres, and $\rho$ is the liquid density.

Show that $\rho$ is about $1200\,\mathrm{kg\,m^{-3}}$ .

$D=2.38\pm0.01\,\mathrm{cm}$ , $T=0.61\pm0.01\,\mathrm{s}$ , $m=48.95\,\mathrm{g}$ .

Rearrange to $\rho=\frac{16\pi m}{D^2T^2g}.$ Substitution gives $\rho=\frac{16\pi(48.95\times10^{-3})}{(2.38\times10^{-2})^2(0.61)^2(9.81)}=1190\,\mathrm{kg\,m^{-3}},$ about $1200\,\mathrm{kg\,m^{-3}}$ .

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Edexcel A-Level Physics A2 5.5.144 Shm Displacement Velocity and Acceleration Equations Questions question 1