1
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is ___________. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
2
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1

The general displacement of a simple harmonic oscillator is $$x = A\sin \omega t$$. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $$t = {T \over \beta }$$. The value of $$\beta$$ is ______________.

3
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1

A particle of mass 250 g executes a simple harmonic motion under a periodic force $$\mathrm{F}=(-25~x)\mathrm{N}$$. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ___________ cm.

4
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.