1
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1 A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.

2
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1  A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $$\frac{\pi}{\sqrt x}$$ in SI unit. The value of $$x$$ is ____________.

3
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1 The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $$10 \mathrm{~s}$$. If the metallic bob is immersed in water, then the new time period becomes $$5 \sqrt{x}$$ s. The value of $$x$$ will be ________.

4
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1 The potential energy of a particle of mass $$4 \mathrm{~kg}$$ in motion along the x-axis is given by $$\mathrm{U}=4(1-\cos 4 x)$$ J. The time period of the particle for small oscillation $$(\sin \theta \simeq \theta)$$ is $$\left(\frac{\pi}{K}\right) s$$. The value of $$\mathrm{K}$$ is _________.

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