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A mass- sprin...

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A mass- spring system oscillates such that the mass moves on a rough surface having coefficient of friction μ. It is compressed by a dis†an ce a from its normal length and, on being released, it moves to a dis†an ce b from its equilibrium position. The decrease in amplitude for one half-cycle (-ato b) is

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Q. A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction

μ

. It is compressed by a distance a from its normal length and, on being released, it moves to a distance

b

from its equilibrium position. The decrease in amplitude for one half-cycle

(- a t o b)

Q. A mass on a frictionless surface is attached to a spring. The spring is compressed from its equilibrium position, B , to point A , a distance x from B . Point C is also a distance x from B, but in the opposite direction. When the mass is released and allowed to oscillated freely, at what point or points is its velocity maximized?

Q. The block shown in the figure, is acted on by a spring with spring constant

k

and a weak frictional force of constant magnitude

f

. The block is pulled a distance

x_{0}

from equilibrium position and then released. It oscillates many times and ultimately comes to rest. Show that the decrease of amplitude is the same for each cycle of oscillation.

Q. A block of mass

m = 0.1 k g

is connected to a spring of unknown spring constant

k

. It is compressed to a distance

x

from its equilibrium position and released from rest.
After approaching half the distance

(\frac{x}{2})

from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity

3 m s^{- 1}

. The total initial energy of the spring is :

Q. One end of an elastic spring of natural length

L

and spring constant

k

is fixed to a wall and the other end is attached to a block of mass

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lying on a horizontal frictionless table. The block is moved to a position A, such that the spring is compressed to half its natural length and then released. What is the velocity of the block when it reaches position B, which is at a distance

\frac{3 L}{4}

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