1
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1 A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $$\mathrm{K}_{1}$$ and $$\mathrm{K}_{2}$$. For the frictionless surface, the time period of oscillation of mass $$m$$ is A
$$2\pi \sqrt {{m \over {{K_1} + {K_2}}}}$$
B
$$2\pi \sqrt {{m \over {{K_1} - {K_2}}}}$$
C
$${1 \over {2\pi }}\sqrt {{{{K_1} + {K_2}} \over m}}$$
D
$${1 \over {2\pi }}\sqrt {{{{K_1} - {K_2}} \over m}}$$
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1 Choose the correct length (L) versus square of the time period ($$\mathrm{T}^{2}$$) graph for a simple pendulum executing simple harmonic motion.

A B C D 3
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1 The maximum potential energy of a block executing simple harmonic motion is $$25 \mathrm{~J}$$. A is amplitude of oscillation. At $$\mathrm{A / 2}$$, the kinetic energy of the block is

A
9.75 J
B
37.5 J
C
18.75 J
D
12.5 J
4
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1 For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1 \mathrm{~kg}$, the angular frequency is $\omega_{1}$. When the mass block is $2 \mathrm{~kg}$ the angular frequency is $\omega_{2}$. The ratio $\omega_{2} / \omega_{1}$ is A
$1 / \sqrt{2}$
B
$1 / 2$
C
2
D
$\sqrt{2}$
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