Let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is

(a) at the mean position,

(b) at the maximum stretched position, and

(c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?

Asked by Pragya Singh | 1 year ago |  56

#### 1 Answer

##### Solution :-

Distance travelled by the mass sideways, a = 2.0 cm

Angular frequency of oscillation:

ω = $$\dfrac{\sqrt{k}}{m}$$

$$\dfrac{\sqrt{1200}}{3}$$

$$\sqrt{400}$$

We get,

= 20 rad s-1

(a) As time is noted from the mean position,

Hence, using

x = a sin ωt

We have,

x = 2 sin 20 t

(b) At maximum stretched position, the body is at the extreme right position,

with an initial phase of $$\dfrac{π}{2}$$ rad. Then,

x = $$\dfrac{ a sin (ωt + π) }{2}$$

= a cos ωt

= 2 cos 20 t

(c) At maximum compressed position, the body is at left position,

with an initial phase of $$\dfrac{ 3π}{2}$$ rad.

Then,

x =$$\dfrac{ a sin (ωt + 3π) }{2}$$

= – a cos ωt

= – 2 cos 20 t

Therefore,

The functions neither differ in amplitude nor in frequency. They differ in initial phase.

Answered by Abhisek | 1 year ago

### Related Questions

#### A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction

A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x0 and v0. [Hint: Start with the equation x = a cos (ωt+θ) and note that the initial velocity is negative.]

Class 11 Physics Oscillations View Answer

#### A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is

(a) 5 cm

(b) 3 cm

(c) 0 cm.

Class 11 Physics Oscillations View Answer

#### A circular disc of mass 10 kg is suspended by a wire attached to its centre.

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J = –α θ, where J is the restoring couple and θ the angle of twist).

Class 11 Physics Oscillations View Answer

#### Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals.

Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

Class 11 Physics Oscillations View Answer

#### You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation

You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of

(a) the spring constant k and

(b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.

Class 11 Physics Oscillations View Answer