Home
Class 11
PHYSICS
A 0.950 kg mass hangs vertically from a ...

A 0.950 kg mass hangs vertically from a spring that he a spring constant of 8.50 N /m . The mass is set into vertical oscillations and after 600 s , you find tht the amplitude of the oscillation is `1/10` That of initial amplitude.
What is the damping constant associated with this motion?

Text Solution

Verified by Experts

The amplitude is `A=A_(0) e^(-alphat)`
Divide by `A_(0))` take natural logarithms and solve for `alpha`
`A/(A_(0))=e^(-alphat)impliesl_(n)((A)/(A_(0)))=-alphat`
`impliesalpha=-1/tl_(n)((A)/(A_(0)))`
Since `alpha=(beta)/(2m), "the "beta=2malpha.` Thus,
`beta=-(2m)/(t)l_(n)((A)/(A_(0)))`
Now substituting `0.950kg " for"m,600s.` for t and 0.10 for `((A)/(A_(0)))`
`beta=-(2m)/(t)l_(n)((A)/(A_(0)))=-(2(0.950))/(600)l_(n)0.10`
`=7.3xx10^(-3)kgs^(-1)`
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    SURA PUBLICATION|Exercise NUMERICAL PROBLEMS (3 Marks)|5 Videos

  • OSCILLATIONS

    SURA PUBLICATION|Exercise CREATIVE QUESTIONS (HOTS)|21 Videos

  • OSCILLATIONS

    SURA PUBLICATION|Exercise NUMERICAL PROBLEMS (1 Mark)|10 Videos

  • NATURE OF PHYSICAL WORLD AND MEASUREMENT

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS|241 Videos

  • PROPERTIES OF MATTER

    SURA PUBLICATION|Exercise Value based Questions|5 Videos

Similar Questions

Explore conceptually related problems

Find the time period of the oscillation of mass m in figure a,b,c what is the equivalent spring constant of the pair oif springs in each case?

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 particle of mass 0.50 kg executes a simple harmonic motion under a force F=-(50Nm^-1)x . If it crosses the centre of oscillation with a speed of 10ms^-1 , find the amplitude of the motion.

A spring of spring constant 50 N/m is compressed from its natural position through 1 cm. Find the work done by the spring force on the agency compressing the spring.

A particle having mass 10 g oscillates according to the equation x=(2.0cm) sin[(100s^-1)t+pi/6] . Find the amplitude the time period and the spring constant

The pulley shown in figure has a moment of inertias I about its axis and mass m. find the time period of vertical oscillation of its centre of mass. The spring has spring constant k and the string does not slip over the pulley.

A mass m = 50 g is dropped on a vertical spring of spring constant 500 N/m from a height h= 10 cm as shown in figure (18-E14). The mass sticks to the spring and executes simple harmonic oscillations after that. A concave mirror of focal length 12 cm facing the mass is fixed with its principal axis coinciding with the line of motion of the mass, its pole being at a distance of 30 cm from the free end of the spring. Find the length in which the image of the mass oscillates.

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. spring is now cut into two equal halved and the same mass is suspended fron one of the havles. The period of vertical oscillation is :

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. spring is now cut into two equal halved and the same mass is suspended fron one of the havles. The period of vertical oscillation is :

A block of known mass is suspended from a fixed support through a ligh spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?