Simple Harmonic Oscillation

A pendulum of length $4a$ is suspended from the origin O. Its swing is constrained by two baffles shaped as inverted cycloids, described parametrically by $x = a(\varphi - \sin\varphi)$ and $y = a(1-\cos\varphi)$. The pendulum string wraps around these baffles as it swings. The y-axis points downwards.

A 2.0 kg object hangs from a spring. When an additional 0.3 kg object is hung below it, the spring stretches a further 2.0 cm. The 0.3 kg object is then removed and the 2.0 kg object is set into vibration.

A particle undergoes simple harmonic motion about $x = 0$. At $t = 0$ its displacement is $x = 0.37$ cm and its velocity is zero. The vibration frequency is $0.25$ Hz.

A tuning fork vibrates in simple harmonic motion at a frequency of $1000$ Hz, and the tip of one of its prongs has an amplitude of $0.40$ mm.

A vibrating spring oscillator has a mechanical energy of $1.0$ J, an amplitude of $0.10$ m, and a maximum speed of $1.0$ m/s.

A 3.0 kg particle has a displacement given by

A 5.0 kg object moves on a frictionless horizontal surface under a spring of force constant $1.0 \times 10^3$ N/m. The object is displaced to 50 cm from the equilibrium position and given an initial speed of 10 m/s directed toward the equilibrium position.