Question 1 :
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is {tex} 15\ { cm } / { sec } {/tex} and the period is {tex}628{/tex} milli-seconds. The amplitude of the motion in<br>centimeters is<br>

Question 2 :
A flat horizontal platform moves up and down in S.H.M. with an amplitude of 1 cm. A small object is placed on the platform. What is the maximum frequency the platform can have, if the object is not to separate from it during any part of the motion ?<br>

Question 3 :
A small piece of cork in a ripple tank oscillates up and down as ripples pass it. If the ripples travelling at 0.3 m/s have a wavelength of 1.5 &pi; cm and the cork vibrates with an amplitude of 5 mm, the maximum velocity of the cork is -<br>

Question 4 :
The equation of motion of a particle is {tex} \frac { d ^ { 2 } y } { d t ^ { 2 } } + K y = 0 , {/tex} where {tex} K {/tex} is positive constant. The time period of the motion is given by

Question 6 :
The displacement {tex} x {/tex} (in centimeters) of an oscillating particle varies with time (in seconds as) {tex} x = 2 \cos \left( 0.5 \pi t + \frac { \pi } { 3 } \right) . {/tex} The magnitude of the maximum acceleration of the particle in {tex} \mathrm { cms } ^ { - 2 } {/tex} is

Question 7 :
The displacement of a particle varies with time according to the relation. {tex} y = a {/tex} sin {tex} \omega t + b \cos \omega t {/tex}

Question 8 :
The equation of motion of a particle is {tex} x = a \cos ( \alpha t ) ^ { 2 } {/tex} The motion is

Question 9 :
A particle is acted simultaneously by mutually perpendicular SHM {tex} x = a \cos \omega t {/tex} and {tex} y = a \sin \omega t {/tex} The trajectory of motion of the particle will be.

Question 10 :
A person measures the time period of a simple pendulum inside a stationary lift and finds it to be {tex} T . {/tex} If the lift starts accelerating upwards with an acceleration of {tex} \mathrm { g } / 3 , {/tex} the time period of the pendulum will be

Question 11 :
The displacement of a particle is represented by the equation {tex} y = \sin ^ { 3 } \omega t {/tex}. The motion is

Question 12 :
<font>What is the amplitude of wave shown in figure -</font></p> <p> <img style='object-fit:contain' align="bottom" height="98" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0efe075b85f121f54260f" width="273"/> </p>

Question 13 :
The displacement of a particle is represented by the equation {tex} y = 3 \cos \left( \frac { \pi } { 2 } - 2 \omega t \right) . {/tex} The motion of the particle is

Question 14 :
<font>The displacement of an elastic wave is given by the function y = 3 sin wt + 4 cos wt where y is in cm and t is in s. The resultant amplitude is</font></p>

Question 15 :
Figure 9.27 shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated in the Fig. 9.27. The SHM of the x-projection of the radius vector of the rotating particle P is <br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d81fb40ed89a522c5ea38dd" />