Simple harmonic systemsAQA A-Level Physics: Mind map

Exam questions on Simple harmonic systems

1. A 0.250 kg mass hangs from a light spring of spring constant 40 N m⁻¹. The mass is pulled down a small distance and released, so that it oscillates vertically with simple harmonic motion.
   The apparatus is taken to the Moon, where the gravitational field strength is smaller, and the oscillation is repeated with the same mass and spring. State and explain the effect on the time period.2 marks
2. A student sets up a simple pendulum in a laboratory using a small dense bob on a light inextensible string. The distance from the point of suspension to the centre of the bob is 0.640 m. The local gravitational field strength is 9.81 N kg⁻¹.
   A pendulum clock keeps correct time at sea level. It is taken to the top of a high mountain, where $g$ is slightly smaller, and its length is not changed. Explain why the clock runs slow.2 marks
3. A uniform U-tube of cross-sectional area $A$ contains liquid of density $\rho$ with a total column length $L$ = 0.360 m. When the liquid in one arm is pushed down by a displacement $x$, the liquid in the other arm rises by $x$, and the unbalanced weight of liquid acting to restore equilibrium is $2\rho A g x$. Viscous effects are negligible.
   Show that the liquid oscillates with simple harmonic motion and that the time period is $T = 2\pi\sqrt{\dfrac{L}{2g}}$.3 marks