Advertisements
Advertisements
प्रश्न
The displacement of a particle is represented by the equation y = sin3ωt. The motion is ______.
पर्याय
non-periodic.
periodic but not simple harmonic.
simple harmonic with period 2π/ω.
simple harmonic with period π/ω.
उत्तर
The displacement of a particle is represented by the equation y = sin3ωt. The motion is periodic but not simple harmonic.
Explanation:
Given the equation of motion is y = sin3ωt
= `(3 sin ωt - 4 sin 3 ωt)/4` .....[∵ sin 3θ = 3 sin θ – 4sin3θ]
⇒ `(dy)/(dt) = ([d/(dt) (3sin ωt) - d/(dt) (4sin3ωt)])/4`
⇒ `4 (dy)/(dt) = 3ωcos ωt - 4 xx [3ωcos 3ωt]`
⇒ `4 xx (d^2y)/(dt^2) = - 3ω^2sin ωt + 12 ωsin3ωt`
⇒ `(d^2y)/(dt^2) = - (3ω^2 sinωt + 12ω^2 sin 3ωt)/4`
⇒ `(d^2y)/(dt^2)` is not proportional to y.
Hence, the motion is not SHM.
As the expression is involved in function, hence it will be periodic.
APPEARS IN
संबंधित प्रश्न
Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S.H.M.
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?
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 small block oscillates back and forth on a smooth concave surface of radius R ib Figure . Find the time period of small oscillation.
A simple pendulum of length l is suspended through the ceiling of an elevator. Find the time period of small oscillations if the elevator (a) is going up with and acceleration a0(b) is going down with an acceleration a0 and (c) is moving with a uniform velocity.
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.
Consider two simple harmonic motion along the x and y-axis having the same frequencies but different amplitudes as x = A sin (ωt + φ) (along x-axis) and y = B sin ωt (along y-axis). Then show that
`"x"^2/"A"^2 + "y"^2/"B"^2 - (2"xy")/"AB" cos φ = sin^2 φ`
and also discuss the special cases when
- φ = 0
- φ = π
- φ = `π/2`
- φ = `π/2` and A = B
- φ = `π/4`
Note: when a particle is subjected to two simple harmonic motions at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures.
What is the ratio of maxmimum acceleration to the maximum velocity of a simple harmonic oscillator?
A body having specific charge 8 µC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______ s.
