Instantaneous angle (in radian) between string of a simple pendulum and vertical is given by θ = π 180 sin 2 π t . Find the length of the pendulum if g = π 2 m s - 2 .

From the given instantaneous angle expression, angular frequency of pendulum is ω = 2 π . Now time period of pendulum is given as T = 2 π l g , where l is length of pendulum and g is acceleration due to gravity at that place. T = 2 π ω = 2 π l g ⇒ 2 π ω = 2 π l g ⇒ l = g ω 2 = π 2 4 π 2 = 0 . 25 m Hence, the length of pendulum is 25 cm .

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A spring mass system has a time period of $2 s$ . What should be the spring constant of spring if the mass of the block is $10 g$ ?

Important Questions on Simple Harmonic Motion

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 12

A body of mass

2 kg

suspended through a vertical spring executes simple harmonic motion of period

4 s .

If the oscillations are stopped and the body hangs in equilibrium find the potential energy stored in the spring.

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 13

A vertical spring-mass system with lower end of spring is fixed made to undergo small oscillations. If the spring is stretched by

25 cm

, energy stored in the spring is

5 J

.Find the mass of the block if it makes

5

oscillations each second.

HARD

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 14

A spring mass system is shown in figure, spring is initially unstretched. A man starts pulling the block with constant force $F$ . Find

(a) The amplitude and the time period of motion of the block

(b) The KE of the block at mean position

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 15

Three spring mass systems are shown in the figure. Assuming gravity free space, find the time period of oscillations in each case. What should be the answer if space is not gravity free?

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 16

Spring mass system is shown in the figure. Find the elastic potential energy stored in each spring when block is at its mean position. Also find the time period of vertical oscillations. The system is in vertical plane.

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 17

Find the length of seconds pendulum at a place where

g = π^{2} m s^{- 2}

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 18

Instantaneous angle (in radian) between string of a simple pendulum and vertical is given by

θ = \frac{π}{180} \sin 2 π t

. Find the length of the pendulum if

g = π^{2} m s^{- 2}

MEDIUM

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 19

A pendulum clock is accurate at a place where

g = 9.8 m s^{- 2}

. Find the value of

g

at another place where clock becomes slow by

24 s

in a day (

24 h

A spring mass system has a time period of 2 s. What should be the spring constant of spring if the mass of the block is 10 g?

Important Questions on Simple Harmonic Motion

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A spring mass system has a time period of $2 s$ . What should be the spring constant of spring if the mass of the block is $10 g$ ?