## Question

####

Two springs of force constants *k*_{1} and *k*_{2} are connected to a mass *m*placed on a horizontal frictionless surface as shown in fig (a) and (b). What is the ratio of the time periods of horizontal oscillation in cases (a) and (b) if *k*_{1} = *k*_{2}?

### Solution

Correct option is
2

In case (a) the spring are connected in series. Therefore, the spring constant of the combination is given by

In case (b) the spring constant of the combination is

#### SIMILAR QUESTIONS

Q1

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?

Q2

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

Q3

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?

Q4

Two identical strings of a stringed musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the string were in unison?

Q5

A horizontal platform is executing simple harmonic motion in the vertical direction of frequency *v*. A block of mass *m* is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?

Q6

A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take *g* = 10 ms^{–2.} ^{ }

Q7

A spring of negligible mass having a force constant *k* extends by an amount *y* when a mass *m* is hung from it. The mass is pulled down a little and released. The system begins to execute simple harmonic motion of amplitude A and angular frequency ω. The total energy of the mass-spring system will be

Q8

A spring has a natural length of 50 cm and a force constant of A body of mass 10 kg is suspended from it and the spring is stretched. If the body is pulled down further stretching the spring to a length of 58 cm and released, it executes simple harmonic motion. What is the net force on the body when it is at its lowermost position of its oscillation? Take *g* = 10 ms^{ –2}.

Q9

A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. When the turntable is rotated an angular frequency of 10 rad s^{–1}, the length of the spring becomes 40 cm. what is the force constant of the spring? ^{ }

Q10

Two springs of force constants *k*_{1} and *k*_{2} are connected to a mass *m* as shown in fig (a) and (b). What is the ratio of the time periods of vertical oscillation in cases (a) and (b) if *k*_{1} = *k*_{2}?