Advertisements
Advertisements
Question
The ear-ring of a lady shown in figure has a 3 cm long light suspension wire. (a) Find the time period of small oscillations if the lady is standing on the ground. (b) The lady now sits in a merry-go-round moving at 4 m/s1 in a circle of radius 2 m. Find the time period of small oscillations of the ear-ring.
Advertisements
Solution
Given,
Length of the long, light suspension wire, l = 3 cm = 0.03 m
Acceleration due to gravity, `g = 9.8 "ms"^(- 2)`
(a)Time Period \[\left( T \right)\] is given by ,
\[T = 2\pi\sqrt{\left( \frac{l}{g} \right)}\]
\[ = 2\pi\sqrt{\left( \frac{0 . 03}{9 . 8} \right)}\]
\[ = 0 . 34 \text { second}\]
(b) Velocity of merry-go-round, v = 4 `"ms"^(- 1)`
Radius of circle, r = 2 m
As the lady sits on the merry-go-round, her earring experiences centripetal acceleration.
Centripetal acceleration (a) is given by,
\[a = \frac{v^2}{r} = \frac{4^2}{2} = 8 m/ s^2\]
Resultant acceleration (A) is given by ,
\[A = \sqrt{\left( g^2 + a^2 \right)}\]
\[ = \sqrt{\left( 96 . 04 + 64 \right)}\]
\[ = 12 . 65 m/ s^2\]
Time Period,
\[T = 2\pi\sqrt{\left( \frac{l}{A} \right)}\]
\[= 2\pi\sqrt{\left( \frac{0 . 03}{12 . 65} \right)}\]
\[ = 0 . 30 \text { second }\]
APPEARS IN
RELATED QUESTIONS
A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.
Which of the following example represent periodic motion?
An arrow released from a bow.
A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
A particle of mass m is attatched to three springs A, B and C of equal force constants kas shown in figure . If the particle is pushed slightly against the spring C and released, find the time period of oscillation.
The maximum speed of a particle executing S.H.M. is 10 m/s and maximum acceleration is 31.4 m/s2. Its periodic time is ______
A simple pendulum is inside a spacecraft. What will be its periodic time?
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The rotation of the earth about its axis.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
A motion of an oscillating mercury column in a U-tube.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowermost point.
The displacement time graph of a particle executing S.H.M. is shown in figure. Which of the following statement is/are true?
- The force is zero at `t = (T)/4`.
- The acceleration is maximum at `t = (4T)/4`.
- The velocity is maximum at `t = T/4`.
- The P.E. is equal to K.E. of oscillation at `t = T/2`.
What are the two basic characteristics of a simple harmonic motion?
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.
