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प्रश्न
A small creature moves with constant speed in a vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a sample harmonic motion?
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उत्तर
Yes, its shadow on a horizontal plane moves in simple harmonic motion. The projection of a uniform circular motion executes simple harmonic motion along its diameter (which is the shadow on the horizontal plane), with the mean position lying at the centre of the circle.
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संबंधित प्रश्न
Show variation of displacement, velocity, and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from the extreme position.
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?
A particle executes simple harmonic motion. If you are told that its velocity at this instant is zero, can you say what is its displacement? If you are told that its velocity at this instant is maximum, can you say what is its displacement?
The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is
A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude
A pendulum clock keeping correct time is taken to high altitudes,
The motion of a torsional pendulum is
(a) periodic
(b) oscillatory
(c) simple harmonic
(d) angular simple harmonic
A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a second pendulum at a place where g = π2 m/s2.
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.
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.
A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of 45° with the X-axis. The two motions are given by x = x0 sin ωt and s = s0 sin ωt. Find the amplitude of the resultant motion.
A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period is ____________.
The length of a second’s pendulum on the surface of the Earth is 0.9 m. The length of the same pendulum on the surface of planet X such that the acceleration of the planet X is n times greater than the Earth is
What is an epoch?
What is meant by simple harmonic oscillation? Give examples and explain why every simple harmonic motion is a periodic motion whereas the converse need not be true.
A body oscillates with SHM according to the equation x = 5 cos `(2π"t" + π/4)`. Its instantaneous displacement at t = 1 sec is:
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.
Displacement vs. time curve for a particle executing S.H.M. is shown in figure. Choose the correct statements.
- Phase of the oscillator is same at t = 0 s and t = 2s.
- Phase of the oscillator is same at t = 2 s and t = 6s.
- Phase of the oscillator is same at t = 1 s and t = 7s.
- Phase of the oscillator is same at t = 1 s and t = 5s.
A container consist of hemispherical shell of radius 'r ' and cylindrical shell of height 'h' radius of same material and thickness. The maximum value h/r so that container remain stable equilibrium in the position shown (neglect friction) is ______.
