Simple Harmonic Motion and Uniform Circular Motion

Define simple harmonic motion. Show that the motion of point projection of a particle performing circular motion, on any diameter, is circular motion.

The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution are indicated in the figure. Obtain the simple harmonic motions of the x-projection of the radius vector of the rotating particle P in this case.

The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution are indicated in the figure. Obtain the simple harmonic motions of the x-projection of the radius vector of the rotating particle P in this case.

Suppose a particle P is moving uniformly on a circle of radius A with the angular speed $\omega$ . The sense of rotation is anticlockwise. If the $t=0$ , it  makes an angle of $\varphi$ with the positive direction of the x-axis. In time $t$, it will cover a further angle $\omega t$.What is the projection of position vector on the X-axis at time $t$.

If we tie a stone to the end of a string and move it with a constant angular speed in a horizontal plane about fixed point, the stone would perform a : 

In the given figure it corresponds to a circular motion. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on figure?

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P.

Plot the corresponding reference circle for $\mathrm{x}=-2\sin (3\mathrm{t}+\mathrm{\pi }/3)$ simple harmonic motion. Indicate the initial $(\mathrm{t} = 0)$ position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (x is in $\mathrm{cm}$ and t is in $\mathrm{s}$).

In the given figure it corresponds to circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on the figure?

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P.

Cotyledons are also called-

A particle is moving in a uniform circular motion on a horizontal surface. Particle's position and velocity at time $t=0$ are shown in the figure in the coordinate system. Which of the indicated variable on the vertical axis is/are correctly matched by the graph(s) shown alongside for particle's motion?

A stone is swinging in a horizontal circle $0.8 \mathrm{m}$ in diameter, at $30 \mathrm{rev} {\min }^{-1}$. A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? What is the frequency?

A particle is moving in a uniform circular motion on a horizontal surface. Particle position and velocity at time $t=0$ are shown in the figure in the coordinate system. Which of the indicated variable on the vertical axis is incorrectly matched by the graph shown alongside for particle's motion-