English
Karnataka Board PUCPUC Science Class 11

Displacement versus time curve for a particle executing S.H.M. is shown in figure. Identify the points marked at which (i) velocity of the oscillator is zero, (ii) speed of the oscillator is maximum.

Advertisements
Advertisements

Question

Displacement versus time curve for a particle executing S.H.M. is shown in figure. Identify the points marked at which (i) velocity of the oscillator is zero, (ii) speed of the oscillator is maximum.

Short/Brief Note
Advertisements

Solution

In SHM y-t graph, zero displacement values correspond to the mean position; where the velocity of the oscillator is maximum.

Whereas the crest and troughs represent extreme positions, where displacement is maximum and velocity of the oscillator is minimum and is zero. Hence,

  1. A, C, E and G are either crests or trough having zero velocity.
  2. Speed is maximum at mean positions represented by B, D, F, and H paints.
shaalaa.com
Energy in Simple Harmonic Motion
  Is there an error in this question or solution?
Chapter 14: Oscillations - Exercises [Page 102]

APPEARS IN

NCERT Exemplar Physics Exemplar [English] Class 11
Chapter 14 Oscillations
Exercises | Q 14.19 | Page 102

RELATED QUESTIONS

A particle executes simple harmonic motion with an amplitude of 10 cm. At what distance from the mean position are the kinetic and potential energies equal?


The equation of motion of a particle started at t = 0 is given by x = 5 sin (20t + π/3), where x is in centimetre and in second. When does the particle
(a) first come to rest
(b) first have zero acceleration
(c) first have maximum speed?


Consider a particle moving in simple harmonic motion according to the equation x = 2.0 cos (50 πt + tan−1 0.75) where x is in centimetre and t in second. The motion is started at t = 0. (a) When does the particle come to rest for the first time? (b) When does he acceleration have its maximum magnitude for the first time? (c) When does the particle come to rest for the second time ?


The pendulum of a clock is replaced by a spring-mass system with the spring having spring constant 0.1 N/m. What mass should be attached to the spring?


A block of mass 0.5 kg hanging from a vertical spring executes simple harmonic motion of amplitude 0.1 m and time period 0.314 s. Find the maximum force exerted by the spring on the block.


A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 4 s. If the oscillations are stopped and the body hangs in equilibrium find the potential energy stored in the spring.


Consider the situation shown in figure . Show that if the blocks are displaced slightly in opposite direction and released, they will execute simple harmonic motion. Calculate the time period.


A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, find the frequency and the amplitude of the motion.


Show that for a particle executing simple harmonic motion.

  1. the average value of kinetic energy is equal to the average value of potential energy.
  2. average potential energy = average kinetic energy = `1/2` (total energy)

Hint: average kinetic energy = <kinetic energy> = `1/"T" int_0^"T" ("Kinetic energy") "dt"` and

average potential energy = <potential energy> = `1/"T" int_0^"T" ("Potential energy") "dt"`


When a particle executing S.H.M oscillates with a frequency v, then the kinetic energy of the particle? 


When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is ______.


A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is ______.


Motion of an oscillating liquid column in a U-tube is ______.


Draw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.


A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it was held in hand.

What is the amplitude of oscillation?


A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = A sin`(pit)/90`. The ratio of kinetic to the potential energy of this particle at t = 210s will be ______.


The total energy of a particle, executing simple harmonic motion is ______.

where x is the displacement from the mean position, hence total energy is independent of x.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×