Question

The mass m shown in figure is displaced vertically by a small amount and released. If the system oscillates with a period of 2 seconds, the value of the spring constant k is

                                                              

Solution

Correct option is

 

If the mass is displaced by a small amount x, the restoring on it is F = kx +kx = 2kx. Therefore, time period is

                           

SIMILAR QUESTIONS

Q1

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

Q2

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?

Q3

 

A simple harmonic motion is given by the equation 

               

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

Q4

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

                                                   

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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 when they are stretched by the same force is

Q10

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