Question

A body executing linear simple harmonic motion has a velocity of 3 cms–1when its displacement is 4 cm and a velocity of 4 cms–1 when its displacement is 3 cm. what is the amplitude of oscillation?  

Solution

Correct option is

5 cm

 

Is SHM, the velocity V at a displacement x is given by   

                        

                      

                        

Also                 

                         

Simultaneous solution of Eqs. (i) and (ii) gives

Amplitude          A = 5 cm

SIMILAR QUESTIONS

Q1

A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

Q2

Two springs of force constants k1 and k2 are connected as shown in figure. The time period of vertical oscillations of mass m is given by

                                                                

Q3

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1 : 2 : 3. What is the ratio of their fundamental frequencies?

Q4

A particle is in linear simple harmonic motion between two extreme pointsA and B, 10 cm apart (see fig). If the direction from A to B is taken as positive direction, what are signs of displacement x, velocity V and acceleration a, when the particle is at A  

                                                

Q5

A simple harmonic motion of amplitude A has a time period T. The acceleration of the oscillator when its displacement is half the amplitude is

Q6

A body oscillates harmonically with amplitude 0.05 m. At a certain instant of time its displacement is 0.01 m and acceleration is 1.0 ms-2. What is the period of oscillation?

Q7

A tuning fork produces 4 beta per second when sounded with sonometer of vibrating length 48cm. It produces 4 beats per second also when the vibrating length is 50cm. What is the frequency of the tuning fork?

Q8

 

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as 

                         

The magnitude of the maximum acceleration of the particle is 

Q9

A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

Q10

A particle is executing linear simple harmonic motion of amplitude A. what fraction of the total energy is kinetic when the displacement is half the amplitude?