1
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

$$y = A\sin (\pi t + \phi )$$, where time is measured in second. The length of pendulum is

A
97.23 cm
B
25.3 cm
C
99.4 cm
D
406.1 cm
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Motion of a particle in x-y plane is described by a set of following equations $$x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m$$ and $$y = 4\sin (\omega t)\,m$$. The path of the particle will be :

A
circular
B
helical
C
parabolic
D
elliptical
3
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The equation of a particle executing simple harmonic motion is given by $$x = \sin \pi \left( {t + {1 \over 3}} \right)m$$. At t = 1s, the speed of particle will be

(Given : $$\pi$$ = 3.14)

A
0 cm s$$-$$1
B
157 cm s$$-$$1
C
272 cm s$$-$$1
D
314 cm s$$-$$1
4
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

A
6 s
B
8 s
C
12 s
D
36 s
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