Advertisements
Advertisements
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.
Advertisements
उत्तर
In the equation of S.H.M,
x = A sin (ωt + α)
where, (ωt + α) is the phase or phase angle of S.H.M
For a particle starting from extreme position:
Displacement time graph:
Graph:
Velocity-time graph:
Graph:
Acceleration-time graph:
Graph:
APPEARS IN
संबंधित 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?
In measuring time period of a pendulum, it is advised to measure the time between consecutive passage through the mean position in the same direction. This is said to result in better accuracy than measuring time between consecutive passage through an extreme position. Explain.
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 block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?
The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity \[\vec{v}\] . The value of v is
The distance moved by a particle in simple harmonic motion in one time period is
The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is
A pendulum clock that keeps correct time on the earth is taken to the moon. It will run
A particle moves in the X-Y plane according to the equation \[\overrightarrow{r} = \left( \overrightarrow{i} + 2 \overrightarrow{j} \right)A\cos\omega t .\]
The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic
In a simple harmonic motion
(a) the maximum potential energy equals the maximum kinetic energy
(b) the minimum potential energy equals the minimum kinetic energy
(c) the minimum potential energy equals the maximum kinetic energy
(d) the maximum potential energy equals the minimum kinetic energy
Which of the following will change the time period as they are taken to moon?
(a) A simple pendulum
(b) A physical pendulum
(c) A torsional pendulum
(d) A spring-mass system
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.
The pendulum of a certain clock has time period 2.04 s. How fast or slow does the clock run during 24 hours?
A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes π/3 seconds to complete one oscillation. Find the acceleration of the elevator.
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.
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.
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 frequency of simple harmonic motion.
Write short notes on two springs connected in parallel.
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.
Describe Simple Harmonic Motion as a projection of uniform circular motion.
A simple harmonic motion is given by, x = 2.4 sin ( 4πt). If distances are expressed in cm and time in seconds, the amplitude and frequency of S.H.M. are respectively,
A body oscillates with SHM according to the equation x = 5 cos `(2π"t" + π/4)`. Its instantaneous displacement at t = 1 sec is:
A spring is stretched by 5 cm by a force of 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is ______.
The displacement of a particle is represented by the equation y = sin3ωt. The motion is ______.
The velocities of a particle in SHM at positions x1 and x2 are v1 and v2 respectively, its time period will be ______.
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)
