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Potential Energy of an Object at a Height

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A block of mass 0.1kg is connected to an elastic spring of spring cons†an t 640N/m and oscillates in a damping medium of damping cons†an t 10^{-2 ^{}}kg/s. The system dissipates its energy gradually. The time taken for its mechanical energy ofvibration to drop to half of its initial value is?

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Q. A block of mass

0.1 k g

is connected to an elastic spring of spring constant

640 N m^{- 1}

and oscillates in a damping medium of damping constant

10^{- 2} k g s^{- 1}

. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to:

Q. For the damped oscillator shown in Fig, the mass of the block is

200 g, k = 80 N m^{- 1}

and the damping constant

b

40 g s^{- 1}

Calculate.
(a) The period of oscillation,
(b) Time period for its amplitude of vibrations to drop to half of its initial value
(c) The time for the mechanical energy to drop to half initial value.

Q. A block of mass

2 kg

connected to a spring of spring constant

8 {Nm}^{- 1}

is allowed to oscillate on a rough horizontal surface. If the system experiences a damping force

= 0.230 \times

velocity, then the time required for the amplitude of resulting oscillation to fall to half of its initial value is

Q. In damped oscillation mass is

1 k g

and spring constant

= 100 N / m

, damping coefficeint

= 0.5 k g s^{- 1}

. If the mass displaced by

10 c m

from its mean position then what will be the value of its mechanical energy after

4

Q. A block of mass

200

g executing SHM under the influence of a spring of spring constant

k = 90 N m^{- 1}

and a damping constant

b = 40 g s^{- 1}

. Time taken for its amplitude of vibrations to drop to half of its initial values (Given, In

(1 / 2) = - 0.693)

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Potential Energy of an Object at a Height

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