1
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extreme position (A) is given by

A
B
C
D
2
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $$x=\frac{A}{2}$$ and it moves along positive x-axis. The displacement of particle in time t is $$x = A\sin (wt + \delta )$$, then the value of $$\delta$$ will be

A
$$\frac{\pi}{2}$$
B
$$\frac{\pi}{3}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{\pi}{6}$$
3
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1

For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the projection of OP on the $$x$$-axis at time $$t$$ is

A
$$x(t)=\operatorname{cos}\left(\omega t-\frac{\pi}{6} \omega\right)$$
B
$$x(t)=\operatorname{cos}(\omega t)$$
C
$$x(t)=r \cos \left(\omega t+\frac{\pi}{6}\right)$$
D
$$x(t)=r \sin \left(\omega t+\frac{\pi}{6}\right)$$
4
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
$${1 \over {2\pi }}\sqrt {{{{K_1} - {K_2}} \over m}}$$
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