A particle executes simple harmonic motion with a time period \(T.\) It starts at its equilibrium position at \(t=0.\) How will the graph of its kinetic energy \((KE)\) versus time \((t)\) look like?

1.
2.
3.
4.

A particle executes SHM, the graph of velocity as a function of displacement is:
1. A circle
2. A parabola
3. An ellipse
4. A helix

Given below are two statements: 

A particle executes SHM from the mean position with amplitude '\(a\)' and time period \(T\). The displacement of the particle when its speed is half of the maximum speed is \(\frac{\sqrt{x}}{2}a\). The value of \(x\) is:
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)

The time period of a simple pendulum is \(T\). The time taken to complete \(\dfrac{5}{8}\) oscillations starting from the mean position is \(\dfrac{\alpha }{\beta}T\). The value of \(\alpha \) is:

A pendulum made of a uniform wire of cross-sectional area \(A\) has time period \(T\). When an additional mass \(M\) is added to its bob, the time period changes to \(T_M\). If the Young’s modulus of the material of the wire is \(Y\) then \(\frac{1}{Y}\) is equal to:
(\(g=\) gravitational acceleration)
1. \( \left[\left(\frac{{T}_{{M}}}{{T}}\right)^2-1\right] \frac{{Mg}}{{A}} \)
2. \(\left[1-\left(\frac{{T}_{{M}}}{{T}}\right)^2\right] \frac{{A}}{{Mg}} \)
3. \(\left[1-\left(\frac{{T}}{{T}_{{M}}}\right)^2\right] \frac{{A}}{{Mg}} \)
4. \(\left[\left(\frac{{T}_{{M}}}{{T}}\right)^2-1\right] \frac{{A}}{{Mg}}\)

For a simple pendulum, a graph is plotted between its kinetic energy (\(KE\)) and potential energy (\(PE\)) against its displacement \(d\). Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

1.		2.
3.		4.

A particle performs simple harmonic motion with amplitude \(A\). Its speed is tripled at the instant that it is at a distance \(\frac{2A}{3}\) from the equilibrium position. The new amplitude of the motion is: 
1. \( \frac{A}{3} \sqrt{41} \)
2. \(3 \mathrm{A} \)
3. \(A \sqrt{3} \)
4. \(\frac{7 A}{3}\)

An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross-section \(A.\) Young modulus of the material of the wire is \(Y.\) If the mass is pulled down slightly, its frequency of oscillation along the vertical direction is:

If the time period of a \(2\) m long simple pendulum is \(2\) s, the acceleration due to gravity at the place where the pendulum is executing simple harmonic motion is:
1. \(\pi^{2}\) m/s²
2. \(2\pi^{2}\) m/s²
3. \(9.8\) m/s²
4. \(16\) m/s²