Which one of the following equations does not represent SHM, x = displacement, and t = time? Parameters a, b and c are the constants of motion.

(1) x = a sin bt

(2) x = a cos bt + c

(3) x = a sin bt + c cos bt

(4) x = a sec bt + c cosec bt

Two mutually perpendicular simple harmonic vibrations of the same frequency superimpose on each other. The amplitude of the two vibrations is different and they are different from each other in phase. The resultant of superposition is

1.  Parabola

2.  Straight line

3.  Elliptical

4.  Circular

Simple harmonic motion is an example of:

The function ${\sin }^2\left(\omega t\right)$ represents:

1.  An SHM with a period of $\frac{2\mathrm{\pi }}{\mathrm{\omega }}$

2.  An SHM with a period of $\frac{\mathrm{\pi }}{\mathrm{\omega }}$

3.  A periodic motion but not SHM with a period of $\frac{2\mathrm{\pi }}{\mathrm{\omega }}$

4.  A periodic motion but not SHM with a period of $\frac{\mathrm{\pi }}{\mathrm{\omega }}$

A particle moves on a circular path with uniform speed about the origin. The \((x-t)\) graph will be:
(\(x:\) value of \(x-\)coordinate; \(t-\)time)

1.		2.
3.		4.

A simple pendulum attached to the ceiling of a stationary lift has a time period of 1 s. The distance y covered by the lift moving downward varies with time as y = 3.75 ${\mathrm{t}}^2$, where y is in meters and t is in seconds. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, then the time period of the pendulum will be:

A particle moves according $\mathrm{x}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(6<mspace\; width="1em"></mspace>\mathrm{cm}\right)<mspace\; width="1em"></mspace>\cos \left(\frac{\mathrm{\pi }}{2}\mathrm{t}\right)$. Average velocity of the particle in the time interval between t = 0 to t = 3 s is

1.  1 cm/s

2.  3.5 cm/s

3.  2 cm/s

4.  6 cm/s

Given below are two statements: 

Which of the following examples represents periodic motion?

The figure depicts four \(({x\text-t})\) plots for the linear motion of a particle.

(a)
(b)
(c)
(d)

Which of the following is true​​​​?