A simple pendulum oscillates with an amplitude of $5 \ cm$ and has a phase angle of 10°. Which of the below options possibly shows the equation of motion for the simple pendulum?

A spring-mass system is set into motion by stretching the spring to the right of its equilibrium position and then released.

Which of the below options shows the correct velocity-time graphs for the system after it is released?

A simple harmonic oscillator moves according to the equation $y(t)=7 \cos⁡\left(\dfrac{πt}{4} + \dfrac{π}{6}\right)$.

When will the oscillator be $2$ units away from the starting position after it starts oscillating from $t=0$?

A block of mass $2.5 \ kg$ is attached to a spring of constant $20 \ N/m$. The system is then set into Simple Harmonic Motion by compressing the spring by $4 \ cm$. What is the maximum velocity that the block can have during its motion?

Look at the position-time graph for a simple pendulum.

Find the value of time $t$ when the velocity of the simple pendulum reverses its direction for the $1st$ time.

The equation of motion for a simple harmonic oscillator is given by the relationship,

$x(t)=x_o \sin⁡(ωt+ϕ)$

Derive an expression for the time-dependent acceleration $a(t)$ of the simple harmonic oscillator and thus work out the acceleration at time $t = π/ω$.

Look at the below spring-mass system.

If the spring is displaced slightly to the right, as shown above, then what is the angular frequency $ω$ of the system?

The graph represents the potential energy $PE$ of a system as a function of its position $x$.

When the system is displaced slightly from its equilibrium position $(x_l ≤ x ≤ x_r)$, it oscillates approximately as a simple harmonic oscillator. Which of the below statements is true regarding the system?

The differential equation of a rotating system is given as:

$m \dfrac{d^2 θ}{dt^2} = -j^2 \ θ$

Where $m$ is the mass of the system, $θ$ is the angle of rotation, and $j$ is a positive constant. What is the frequency of the rotating system?

A spring-block system is shown below.

When this system is in equilibrium, the spring is compressed from its natural length. The spring is then compressed by another $4 \ cm$ and then released. What is the velocity of the block when it passes through its equilibrium position?

A simple pendulum satisfies the differential equation:

$\dfrac{d^2 x}{dt^2} = -\dfrac{g}{l} \ x$

The graph below shows the variation of the time period squared with the length of the pendulum.

What is the value of $g$ in $m/s^2$?

If $v(t)=-v_o \sin⁡ \dfrac{2πt}{T}$ for a simple harmonic oscillator starting from $x(t=0) = \dfrac{v_o \ T}{2π}$ (where $v_o>0$, and $T$ is the time period of the oscillator), then what is the total distance traveled by the oscillator from time $t=0$ to $t=\dfrac{4T}{3}$?