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Further Mechanics and Thermal Physics

Simple harmonic systems

  • 8 things to know
  • Papers 2 and 3

Overview

The mass-spring system and the simple pendulum, energy in SHM, damping, and the two required practicals.

What you need to know

Answer each one before you reveal it.

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Numbers

What is the time period of a mass-spring system, and what does it depend on?

Numbers

What small-angle approximation is used, and when does a pendulum truly show SHM?

Numbers

Why is the potential energy curve parabolic, and how does kinetic energy vary with time?

Numbers

Why does kinetic energy vary at twice the frequency of displacement, and what is damping?

Evaluation

In the mass-spring practical, what is plotted and what does the gradient give?

Evaluation

In the pendulum practical, what is plotted and what does the gradient give?

Evaluation

Why time many oscillations rather than one in the mass-spring and pendulum practicals?

Numbers

What are the two systems used in Required Practical 7 to investigate simple harmonic motion?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the formula for the time period of a mass-spring system undergoing simple harmonic motion.

    Model answer

    T = 2π√(m/k), where T is the time period, m is the mass, and k is the spring constant.

  2. 2

    In the equation T = 2π√(m/k) for a mass-spring system, what does each symbol represent?

    Model answer

    T is the time period, m is the mass attached to the spring, and k is the spring constant.

  3. 3

    State the formula for the time period of a simple pendulum undergoing simple harmonic motion.

    Model answer

    T = 2π√(l/g), where T is the time period, l is the length of the pendulum, and g is the gravitational field strength.

  4. 4

    In the equation T = 2π√(l/g) for a simple pendulum, identify what each variable represents.

    Model answer

    T is the time period, l is the length of the pendulum (from pivot to centre of mass of bob), and g is the gravitational field strength.

  5. 5

    What factors does the time period of a mass-spring system depend on, and what factor does it not depend on?

    Model answer

    The time period depends on mass and spring constant, but is independent of amplitude.

  6. 6

    If the amplitude of oscillation of a mass-spring system is doubled, what happens to the time period?

    Model answer

    The time period remains unchanged, as it is independent of amplitude.

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