Simple Harmonic Oscillation

A thin rod of length $L$ and mass $m$ is suspended at its midpoint from a long wire. Its period of angular simple harmonic motion is $T_a$. An irregularly shaped object, object X, is then hung from the same wire, and its period is found to be $T_b$.

A uniform meter stick of length L swings as a physical pendulum about a pivot point at one of its ends. The distance from the pivot to the stick's center of mass is h.

Block 1 of mass $m_1$ slides on a frictionless elevated surface at speed $v_{1i}$. It undergoes a one-dimensional elastic collision with a stationary block 2. After the collision, block 2, which is attached to a spring of constant $k$, oscillates in SHM with period $T$. Block 1 slides off the surface, which is at a height $h$ above the ground.

A block is on a horizontal surface that is moving back and forth with simple harmonic motion (SHM) of frequency $f$. The coefficient of static friction between the block and the surface is $\mu_s$.

Two springs are joined and connected to a block of mass $m$ that is set oscillating over a frictionless floor. The springs each have a spring constant $k$.

A block of mass $m$ (and weight $W=mg$) can slide without friction on an incline at an angle $\theta$. It is connected to the top of the incline by a massless spring of unstretched length $L_0$ and spring constant $k$.

Two blocks, with masses $m$ and $M$, are arranged on a horizontal frictionless surface as shown. The larger block $M$ is attached to a horizontal spring with spring constant $k$. The smaller block $m$ rests on top of $M$. The coefficient of static friction between the two blocks is $\mu_s$. The system undergoes simple harmonic motion (SHM).

A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20 N·m is required to rotate the sphere through an angle of 0.85 rad and then maintain that orientation.

The balance wheel of an old-fashioned watch oscillates with angular amplitude $\pi$ rad and period 0.500 s.

A uniform board of mass $m$ and length $L$ is hinged at one end. The other end is attached to a vertical spring with spring constant $k$. After a penguin dives off, the board oscillates with a small amplitude.