Circle the correct word or statement that completes each sentence. As pendulum length increases, the period of harmonic motion increases / decreases / remains the same. As pendulum mass increases, the period of harmonic motion increases / decreases / remains the same. As gravity (Jupiter) on the pendulum increases, the period of harmonic motion increases / decreases / remains the same. A pendulum attains maximum velocity at the equilibrium position / at maximum amplitude. A pendulum attains minimum velocity at the equilibrium position / at maximum amplitude. A pendulum attains maximum acceleration at the equilibrium position / at maximum amplitude. A pendulum attains minimum acceleration at the equilibrium position / at maximum amplitude. A pendulum attains maximum PE (potential energy) at the equilibrium position / at maximum amplitude.

3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W3 Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (do/dt) 2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01-02/2, for 0 < 1. (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM ML²/6. =

Macmillan Learning A simple pendulum oscillates between +4.0° (as measured from the vertical) on the surface of Earth. The length of the pendulum is 0.30 m. Define full as the amount of time that the pendulum takes to move from 4.0° to -4.0°, and define thalf as the amount of time that the pendulum takes to move from 2.0° to -2.0° during the same swing. tfull Compare the two times by determining the ratio thalf tfull = thalf

A 1.31 m long thin uniform rod is pivoted at one point so that it oscillates like a physical pendulum. Compare the angular frequency of this physical pendulum with a simple pendulum of the same length, both oscillating near the earth's surface. Round off your final answer to two decimal places. Hint: physical (0 simple Add your answer

A mass-spring oscillator is created. It has a period of 6 seconds and an amplitude of 2 cm.When a 0.70 kg-object is attached to the spring hung vertically, it stretches 0.15 m from theequilibrium position. (The following questions can be answered in either order depending onmethod )A. What is the maximum speed of the oscillator?B. What is mass hanging in the spring?