Advertisements
Advertisements
प्रश्न
Three simple harmonic motions of equal amplitude A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.
Advertisements
उत्तर
It is given that three S.H.M.s of equal amplitudes A and equal time periods are combined in the same direction.
Let
\[Y_1 , Y_2 \text { and } Y_3\] be the three vectors representing the motions, as shown in the figure given below.
According to the question:
\[\text { Angle between } Y_1 \text { and } Y_2 = 60 ^\circ\]
\[\text { Angle between } Y_2 \text{ and } Y_3 = 60 ^\circ\]
By using the vector method, we can find the resultant vector.
Resultant amplitude = Vector sum of the three vectors
= A + A cos 60° + A cos 60°
\[= A + \frac{A}{2} + \frac{A}{2} = 2A\]
APPEARS IN
संबंधित प्रश्न
Can simple harmonic motion take place in a non-inertial frame? If yes, should the ratio of the force applied with the displacement be constant?
It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.
A student says that he had applied a force \[F = - k\sqrt{x}\] on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.
The distance moved by a particle in simple harmonic motion in one time period is
A pendulum clock keeping correct time is taken to high altitudes,
A pendulum clock keeping correct time is taken to high altitudes,
For a particle executing simple harmonic motion, the acceleration is proportional to
In a simple harmonic motion
The angle made by the string of a simple pendulum with the vertical depends on time as \[\theta = \frac{\pi}{90} \sin \left[ \left( \pi s^{- 1} \right)t \right]\] .Find the length of the pendulum if g = π2 m2.
A pendulum clock giving correct time at a place where g = 9.800 m/s2 is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.
A uniform rod of length l is suspended by an end and is made to undergo small oscillations. Find the length of the simple pendulum having the time period equal to that of the road.
A particle is subjected to two simple harmonic motions given by x1 = 2.0 sin (100π t) and x2 = 2.0 sin (120 π t + π/3), where x is in centimeter and t in second. Find the displacement of the particle at (a) t = 0.0125, (b) t = 0.025.
If the inertial mass and gravitational mass of the simple pendulum of length l are not equal, then the time period of the simple pendulum is
Define the time period of simple harmonic motion.
State the laws of the simple pendulum?
Describe Simple Harmonic Motion as a projection of uniform circular motion.
Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is ______.
- simple harmonic motion.
- non-periodic motion.
- periodic motion.
- periodic but not S.H.M.
A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its midpoint. The bob is displaced slightly, perpendicular to the plane of the rod and string. The period of small oscillations of the system in the form `(pix)/10` is ______ sec. and the value of x is ______.
(g = 10 m/s2)
Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, and c are positive constants?
