Home
Class 11
PHYSICS
A small body of mass m is connected to t...


A small body of mass `m` is connected to two horizontal spring of elastic constant `k`, natural length `(3d)/(4)`. In the equilibrium position botgh springs are stretched to length `d`, as shown in Fig. What will be the ratio of perod of the motion `((T_b)/(T_a))` If the body is displaced horizontally by a small distance where `T_a` is the time period when the particle owscillates along the line of spring `T_b` is time plane of the figure? Neglect effect of gravity.

Text Solution

Verified by Experts


Initial stretch in both springs `=d-(3d)/(4)=(d)/(4)`
`f_(resteri ng)=k((d)/(4)_x)-k((d)/(4)-x)=2kx`
`impliesT_a=2pisqrt((m)/(k))`
`d'=dsectheta`
`x'=dsectheta-(3d)/(4)=d((1)/(costheta)-(3)/(4))`
Promotional Banner

Topper's Solved these Questions

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Subjective type|2 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Single correct Answer Type|29 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Comprehension|33 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger|11 Videos

  • MISCELLANEOUS KINEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger type|3 Videos

Similar Questions

Explore conceptually related problems

A block of mass m hangs from a vertical spring of spring constant k. If it is displaced from its equilibrium position, find the time period of oscillations.

A rod of mass m and length l is connected by two spring of spring constants k_(1) and k_(2) , so that it is horizontal at equilibrium. What is the natural frequency of the system?

The frequency of oscillations of a mass m connected horizontally by a spring of spring constant k is 4 HZ. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is

A body of mass 20 g connected to a spring of spring constant k, executes simple harmonic motion with a frequency of (5//pi) Hz. The value of spring constant is

A spring of force constant k extends by a length X on loading . If T is the tension in the spring then the energy stored in the spring is

A block of mass m is connected two springs of spring constant 2k annd k , respectively , as shown in the vertical plane. At equilibrium , both springs are compressed by same length. If suddenly lower spring is cut, then acceleration of block, just after spring cut , is

The block of mass m is released when the spring was in its natrual length. Spring constant is k. Find the maximum elongation of the spring.

A spring of spring constant k is cut into n equal parts, out of which r parts are placed in parallel and connected with mass M as shown in figure. The time period of oscillatory motion of mass M is:

In the figure, a block of mass m is rigidly attached to two identical springs of stiffness k each. The other ends of the springs are connected to the fixed wall. When the block is in equilibrium, length of each spring is b, which is greater than the natural length of the spring. The time period of the oscillation of the block if it is displaced by small distance perpendicular to the length of the springs and released. Space is gravity free.

A block of mass m lie on a horizontal smooth surface and connected with the springs at their natural length as shown in figure. When block slightly displaced then find the time period of oscillation.