Simple Harmonic Oscillation

A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance $d$ from the 50 cm mark. The period of oscillation is 2.5 s.

As shown, the pendulum consists of a uniform disk with radius $r = 10.0$ cm and mass $m_d = 500$ g attached to a uniform rod with length $L = 500$ mm and mass $m_r = 270$ g. The rod is pivoted at its upper end.

A block with mass $m$ is connected to two identical masselss spring with hooke's constant $k$, as shown in the figure.

A tuning fork undergoes simple harmonic motion with a frequency of $f = 1000$ Hz. The amplitude of one of its prongs' end is $A = 0.40$ mm.

A vibrating spring-mass oscillator has a mechanical energy $E = 1.0$ J, an amplitude $A = 0.10$ m, and a maximum velocity $v_{max} = 1.0$ m/s.

An accurate astronomical clock with a seconds pendulum is mounted in the basement of the main building of the University. The clock is transferred to the upper storey of the University which is 200 m higher than the basement.

Two pendula begin to swing simultaneously. During the first fifteen oscillations of the first pendulum the other pendulum makes only ten swings.

A pendulum is attached to a board which can fall freely without friction down guide ropes. Before the board is released the pendulum is deflected from the position of equilibrium (Fig. 72).

A pendulum is secured on a cart rolling without friction down an inclined surface. The period of the pendulum on an immobile cart is $T_0$.

A spherical soap bubble of mass $m$ and equilibrium radius $r_0$ is in a vacuum. The bubble is filled with air and undergoes small radial oscillations. Assume the process is isothermal and the surface tension coefficient of the soap film is $\alpha$.