Required Practicals 7–8: Oscillations and Gas Laws

For a mass–spring oscillator, vary mass, displace it modestly and measure the time for many complete oscillations. Divide by the cycle count to obtain T. Plot T² against mass; the ideal gradient is 4π²/k. A real spring has mass, which can give an effective-mass intercept rather than a line exactly through the origin.

For a simple pendulum, measure length from pivot to the bob’s centre of mass, keep a small amplitude and time many cycles through a consistent reference point. Plot T² against length; gradient is 4π²/g. Keep the stand stable and the mass secure. Count full returns to the same position and direction.

Trap a fixed amount of gas, vary its volume using a suitable sealed apparatus and measure absolute pressure. Change volume slowly and allow temperature to re-equilibrate before recording each pressure. Plot p against 1/V for a straight-line test, or inspect whether pV remains constant within uncertainty.

Use total trapped volume, including connecting tubes if significant, and absolute rather than gauge pressure. A pressure gauge reading zero relative to the room does not mean the gas has zero absolute pressure. Check leaks and do not exceed the apparatus pressure limit.

Use an apparatus that allows a trapped gas to change volume while pressure stays approximately atmospheric, such as an appropriate capillary arrangement or a freely moving low-friction piston. Place it in controlled-temperature baths, wait for equilibrium and record volume and temperature.

For fixed amount and pressure, volume is proportional to absolute temperature. Plot V against T in kelvin for an origin test, or V against Celsius temperature to extrapolate towards −273 °C in the ideal model. Keep trapped gas amount fixed and account for non-uniform heating. Merely changing temperature in a sealed rigid vessel tests pressure–temperature behaviour, not Charles’s volume–temperature law.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.