Question

Two bodies M and N of equal masses are suspended from two separate springs of force constants k1 and k2 respectively. If they oscillate with equal maximum velocities, the amplitudes of M and N will be the ratio of

Solution

Correct option is

 

The angular frequencies of the simple harmonic motions of M and Nrespectively are

                         

The maximum velocities of M and N respectively are, V1 = A1ω1 and V2 =A2ω2V1 = V2 if A1ω1 = A2ω2, or

                       

From (i) and (ii) we get  .

SIMILAR QUESTIONS

Q1

 

A transverse wave is represented by 

                   

For what value of λ is the maximum particle velocity equal to twice the wave velocity?

Q2

A pendulum clock keeps correct time at 20oC. The coefficient of linear expansion of pendulum is . If the room temperature increases to 40oC, how many seconds will the clock lose or gain per day?

Q3

A mass m is suspended from a spring of negligible mass. The system oscillates with frequency n. What will be the frequency if a mass 4 m is suspended from the same spring?

Q4

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.17s. The frequency of the wave is

Q5

The kinetic energy of a particle executing S.H.M. is 16 J, when it is at its mean position. If the amplitude of oscillation is 25 cm and the mass of the particle is 5.12 kg, the time period of oscillation is

Q6

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a separation of 1.21 Å between them. The wavelength of the standing wave is

Q7

A body is executing S.H.M. with angular frequency 2 rad s–1. If the amplitude of the motion is 60 mm, the velocity of the body at 20 mm displacement is

Q8

 

A wave is represented by the equation  

                                  

Where x is in metres and t in seconds. The expression represents

Q9

A stretched string of length 1 m, fixed at both ends, having a mass of  kg is under a tension of 20 N. It is plucked at a point situated at 25 cm from one end. The string would vibrate with a frequency of

Q10

A sonometer wire is in unison with a tuning fork. Keeping the tension unchanged, the length of the wire between the bridge is doubled. The tuning fork can still be in resonance with the wire, provided the wire now vibrates in