1
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1

The time period of simple harmonic motion of mass $$M$$ in the given figure is $$\pi \sqrt{\frac{\alpha M}{5 k}}$$, where the value of $$\alpha$$ is _________.

2
JEE Main 2024 (Online) 31st January Morning Shift
Numerical
+4
-1

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2 A}{3}$$. The new amplitude of motion is $$\frac{n A}{3}$$. The value of $$n$$ is ___________.

3
JEE Main 2024 (Online) 29th January Evening Shift
Numerical
+4
-1

A simple harmonic oscillator has an amplitude $$A$$ and time period $$6 \pi$$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $$x=$$ A to $$x=\frac{\sqrt{3}}{2}$$ A will be $$\frac{\pi}{x} \mathrm{~s}$$, where $$x=$$ _________.

4
JEE Main 2024 (Online) 29th January Morning Shift
Numerical
+4
-1

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $$\frac{x}{8}$$, where $$x=$$ _________.