Advertisements
Advertisements
प्रश्न
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.
पर्याय
As x increases k increases.
As x increases k decreases.
As x increases k remains constant.
The motion cannot be simple harmonic.
Advertisements
उत्तर
As x increases k increases.
A body is said to be in simple harmonic motion only when,
F = \[-\]kx ...(1)
where F is force,
k is force constant, and
x is displacement of the body from the mean position.
Given:
F = -k\[\sqrt{x}\]...(2)
On comparing the equations (1) and (2), it can be said that in order to execute simple harmonic motion, k should be proportional to \[\sqrt{x}\] .
Thus, as x increases k increases.
APPEARS IN
संबंधित प्रश्न
A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.
Can the potential energy in a simple harmonic motion be negative? Will it be so if we choose zero potential energy at some point other than the mean position?
Can a pendulum clock be used in an earth-satellite?
The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is
A pendulum clock that keeps correct time on the earth is taken to the moon. It will run
A pendulum clock keeping correct time is taken to high altitudes,
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
A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is 1.67 m/s2?
A small block oscillates back and forth on a smooth concave surface of radius R in Figure. Find the time period of small oscillation.
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 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.
In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be __________.
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
A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is
A simple pendulum has a time period T1. When its point of suspension is moved vertically upwards according to as y = kt2, where y is the vertical distance covered and k = 1 ms−2, its time period becomes T2. Then, T `"T"_1^2/"T"_2^2` is (g = 10 ms−2)
Define the time period of simple harmonic motion.
Write short notes on two springs connected in parallel.
Describe Simple Harmonic Motion as a projection of uniform circular motion.
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.
