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 .

EASY

JEE Main/Advance

IMPORTANT

Earn 100

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.

Important Questions on Simple Harmonic Motion

HARD

JEE Main/Advance

IMPORTANT

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

Question Image

HARD

JEE Main/Advance

IMPORTANT

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?

Question Image

HARD

JEE Main/Advance

IMPORTANT

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.

Question Image

EASY

JEE Main/Advance

IMPORTANT

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}

EASY

JEE Main/Advance

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}

MEDIUM

JEE Main/Advance

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

MEDIUM

JEE Main/Advance

IMPORTANT

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

JEE Main/Advance

IMPORTANT

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.

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.

Important Questions on Simple Harmonic Motion

Learn and Prepare for any exam you want !

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.