Advertisements
Advertisements
Question
A simple pendulum performs S.H.M. of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one-third of its amplitude.
Advertisements
Solution
Data: T= 4 s, x = A/3
The displacement of a particle starting into SHM from the mean position is x = A sin wt = A sin `(2π)/"T"`t
∴ A sin `(2π)/"T"`t = `"A"/3`
∴ `(2π)/"T"`t = sin-1 0.3333 = 19.47° = `19.47xxπ/180`rad
∴ `2/4`t = `19.47/180`
∴ t = `19.47/90` = 0.2163 s
∴ The displacement of the bob will be one-third of its amplitude 0.2163 s after crossing the mean position.
APPEARS IN
RELATED QUESTIONS
Define an ideal simple pendulum.
Obtain the expression for the period of a simple pendulum performing S.H.M.
Answer in brief.
State the law of simple pendulum.
In a second’s pendulum, the mass of Bob is 50 g. If it is replaced by 100 g mass, then its period will be ______.
What is a second pendulum?
A simple pendulum of length I has a bob of mass m. It executes SHM of small amplitude A. The maximum tension in the string is (g = acceleration due to gravity)
The length of a simple pendulum is increased by 44%. The percentage change in its time period is ______.
Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross-section, by 1 mm?
Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is ______.
Two light balls are suspended as shown in figure. When a stream of air passes through the space between them, the distance between the balls will ______.
Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 sec and B completes 8 oscillations in 10 sec. The ratio of the lengths of A and B is ____________.
A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration `("g"/3)`, the time period of the pendulum will be ______.
A pendulum performs S.H.M. with period `sqrt3` second in a stationary lift. If lift moves up with acceleration `"g"/3`, the period of pendulum is ______. (g = acceleration due to gravity)
A simple pendulum has length 'L1'. When its amplitude is 'a' cm, its energy is 'E1'. When length is 2L1, its energy is 'E2' Amplitude is same for both the lengths The relation between E1 and E2 is ______.
Two simple pendulums of lengths 1.44 m and 1.96 m start swinging together. After how many vibrations will they again start swinging together?
The length of a seconds pendulum is 1m on the earth. If the mass and diameter of the planet is double than that of the earth, then the length of the second's pendulum on the planet will be ______
A simple pendulum has a length of 2m and a bob of mass of 100 grams. It is whirled in a horizontal plane. If the string breaks under a tension of 10 N, the angle made by the string with vertical is ______
(g = 10 m/s2)
The maximum kinetic energy of a simple pendulum is 'K'. Its displacement in terms of amplitude 'a', when kinetic energy becomes `(K/2)` is ______.
Define second’s pendulum.
The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is ______.
(N = maximum electron density of lonosphere, g = acceleration due to gravity)
The bob of a simple pendulum performs SHM with period T in air and with period T1 in water Relation between T and T1 is ______.
(neglect friction due to water, density of the material of the bob is = `9/8xx10^3` kgm3, density of water = 1 gcc-1)
Two weights w1 and w2 are suspended from the ends of light string over a smooth fixed pulley. If the pulley is pulled up with acceleration g, the tension in the string will be ______.
The equation of motion in differential form for a seconds pendulum is ______.
At the highest point of its swing, a simple pendulum has maximum potential energy and minimum kinetic energy. What is the total mechanical energy of the pendulum at any point during its motion?
A simple pendulum is used to investigate the dissipation of energy. Which quantity is plotted against time to analyse this dissipation?
A student measures time for 20 oscillations of a simple pendulum as 30 s, 32 s, 35 s and 35 s. If the minimum division in the measuring clock is 1 s, then correct mean time (in second) is ______.
If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is `x/2` times its original time period. Then the value of x is ______.
