1
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1 In the figure given below, a block of mass $$M=490 \mathrm{~g}$$ placed on a frictionless table is connected with two springs having same spring constant $$\left(\mathrm{K}=2 \mathrm{~N} \mathrm{~m}^{-1}\right)$$. If the block is horizontally displaced through '$$\mathrm{X}$$' $$\mathrm{m}$$ then the number of complete oscillations it will make in $$14 \pi$$ seconds will be _____________. 2
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 $\left.\pi=\frac{22}{7}\right)$
3
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 ______________.

4
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.

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