Question

Two bodies A and B of equal masses are suspended from two separate springs of force constants k1 and k2 respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be

Solution

Correct option is

 

The velocity of an oscillating body is maximum when it is at the equilibrium position where the potential energy is zero and the energy is entirely kinetic. At the extreme positions, the kinetic energy is zero and the energy is entirely potential. Therefore, the kinetic energy at equilibrium position = potential energy at extreme positions = total energy. Since the maximum velocities (i.e. velocities at equilibrium position) are equal for the two equal masses, their kinetic energies are also equal = their potential energies at extreme positions where the displacement is maximum = amplitude. If x1 and x2 are amplitudes of bodies A and B, we have

                          

SIMILAR QUESTIONS

Q1

A wooden block is suspended from a spring. Its period for vertical oscillations is T. In a second experiment the same apparatus is laid on a horizontal frictionless table with the free end of the spring fixed to a nail on the table. The block is pulled a little so as to stretch the spring and then released. The mass will   

Q2

The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 parts of hydrogen and 2 parts of oxygen at STP will be.

Q3

A solid brass sphere is hung from a spring whose mass is negligible compared to that of the sphere. The sphere is set into vertical oscillations and its time period is found to be T. The sphere is now completely immersed in a liquid whose density is 1/8th that of brass. The time period of vertical oscillations with the sphere always remaining immersed in the liquid will be equal to

Q4

A heavy metal sphere is suspended from a spring. When pulled down a little and released, it oscillates up and down with a frequency f. If it is taken to the moon (where the acceleration due to gravity is one-sixth that on earth) the frequency of vertical oscillation will

Q5

A mass M attached to a light spring oscillates with a period of 2 seconds. If the mass is increased by 2 kg the period increases by 1 second. What is the value of M?

Q6

 

A simple harmonic motion is given by the equation 

               

Where x is in metres. The amplitude of the motion is

Q7

Figure shows three identical springs A, B, C. When a 4 kg weight is hung on A, it descends by 1 cm. When a 6 kg weight is hung on C, it will descent by

                                                   

Q8

A spring of force constant k is cut into two equal halves. The force constant of each half is

Q9

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young’s modulii are in the ratio of 3:2. They suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

Q10

Two springs A and B have force constants k1 and k2 respectively. The ratio of the work done on A to that done on B in increasing their lengths by the same amount is