SHM Equations — Prelims Questions

A particle executes SHM described by the equation $x(t) = 0.05 \sin(10\pi t + \pi/4)$ meters. What are its amplitude, angular frequency, and initial phase?

A particle performing SHM has a displacement equation $x(t) = 4 \cos(5t + \pi/6)\,\text{cm}$. What is its maximum velocity?

A particle executes SHM with an amplitude of $10\text{ cm}$ and a time period of $2\text{ s}$. What is its maximum acceleration?

A particle starts SHM from its equilibrium position. Its displacement equation is $x(t) = A \sin(\omega t + \phi)$. What is the initial phase $\phi$?

A mass-spring system oscillates with a frequency of $2\text{ Hz}$. If the mass is $0.5\text{ kg}$, what is the spring constant $k$?

A particle in SHM has a displacement $x = 3\text{ cm}$ when its velocity is $4\text{ cm/s}$. If its angular frequency is $2\text{ rad/s}$, what is its amplitude?