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 .

Compound pendulums are made of : (a) A rod of length l suspended through a point located at distance l / 4 from centre of rod. (b) A ring of mass m and radius r suspended through a point on its periphery. (c) A uniform square plate of edge a suspended through a corner. (d) A uniform disc of mass m and radius r suspended through a point r / 2 away from the centre. Find the time period in each case.

Time period compound pendulum is given as T = 2 π I m g h , where I is moment of inertia of the body about axis of rotation, m is mass and h is centre of distance of axis of rotation from centre of mass. a Moment of inertia of rod about point O is given as I O = I COM + m l 4 2 ⇒ I O = m l 2 12 + m l 2 16 = m l 2 12 1 + 3 4 = 7 m l 2 48 . Hence, time period is T = 2 π 7 m l 2 48 m g l 4 = 2 π 7 m l 2 4 48 m g l = 2 π 7 l 12 g = π 7 l 3 g . b Moment of inertia of ring about point O is given as I O = I COM + m r 2 ⇒ I O = m r 2 + m r 2 = 2 m r 2 . Hence, time period is T = 2 π 2 m r 2 m g r = 2 π 2 r g . c Moment of inertia of square about point O is given as I O = I COM + m a 2 2 ⇒ I O = m a 2 6 + m a 2 2 = 2 3 m a 2 . Hence, time period is T = 2 π 2 3 m a 2 m g a 2 = 2 π 2 2 a 3 g . d Moment of inertia of disc about point O is given as I O = I COM + m r 2 = m r 2 2 + m r 2 = 3 2 m r 2 . Hence, time period is T = 2 π 3 2 m r 2 m g r = 2 π 3 r 2 g .

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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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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 17

Find the length of seconds pendulum at a place where

g = π^{2} m s^{- 2}

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IMPORTANT

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}

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IMPORTANT

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

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 20

A pendulum is suspended in a lift and its period of oscillation is $T_{0}$ when the lift is stationary.

(i) What will be the period $T$ of oscillation of pendulum, if the lift begins to accelerate downwards with an acceleration equal to $\frac{3 g}{4}$ ?

(ii) What must be the acceleration of the lift for the period of oscillation of the pendulum to be $\frac{T_{0}}{2}$ ?

HARD

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Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 21

Compound pendulums are made of :

(a) A rod of length $l$ suspended through a point located at distance $l / 4$ from centre of rod.

(b) A ring of mass m and radius $r$ suspended through a point on its periphery.

(d) A uniform disc of mass m and radius $r$ suspended through a point $r / 2$ away from the centre.

Find the time period in each case.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 22

Two compound pendulums are made of:

$(a)$ A disc of radius $r$ and $(b)$ A uniform rod of length $L$ .

Find the minimum possible time period and distance between centre and point of suspension in each case.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise - 1>Q 25

A particle simultaneously participates in two mutually perpendicular oscillations,

x = sinπ t and y = 2 \cos 2 π t

. Write the equation of trajectory of the particle.

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 $10 g$ ?