1
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 $$x=$$ _________.

2
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1

A particle executes simple harmonic motion with an amplitude of $$4 \mathrm{~cm}$$. At the mean position, velocity of the particle is $$10 \mathrm{~cm} / \mathrm{s}$$. The distance of the particle from the mean position when its speed becomes $$5 \mathrm{~cm} / \mathrm{s}$$ is $$\sqrt{\alpha} \mathrm{~cm}$$, where $$\alpha=$$ ________.

3
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$$. If amplitude is $$40 \mathrm{~cm}$$ and kinetic energy at that time is $$200 \mathrm{~J}$$, the value of force constant is $$1.0 \times 10^{x} ~\mathrm{Nm}^{-1}$$. The value of $$x$$ is ____________.

4
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1

A rectangular block of mass $$5 \mathrm{~kg}$$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $$1 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum force exerted by spring on block is _________ N