Advertisements
Advertisements
प्रश्न
What is the ratio of maxmimum acceleration to the maximum velocity of a simple harmonic oscillator?
उत्तर
Let x = A sin ω is the displacement function of SHM.
Velocity, `v = (dx)/(dt) = Aω cosωt`
`v_max = Aω |cos ωt|_"max"`
= `Aω xx 1`
= `ωA` [∵ |cos ωt|max = 1] ......(i)
Acceleration, `a = (dv)/(dt) = - ωA * ωsinωt`
= `- ω^2A sinωt`
`|a_max| = |(- ω^2A)(+1)|` ......[∵ (sin ωt)max = 1]
`|a_max| = ω^2A` .......(ii)
From equations (i) and (ii), we get
`v_max/a_max = (ωA)/(ω^2A) = 1/ω`
⇒ `a_max/v_max = ω`
APPEARS IN
संबंधित प्रश्न
State the differential equation of linear simple harmonic motion.
Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S.H.M.
Can a pendulum clock be used in an earth-satellite?
The force acting on a particle moving along X-axis is F = −k(x − vo t) where k is a positive constant. An observer moving at a constant velocity v0 along the X-axis looks at the particle. What kind of motion does he find for the particle?
A particle executes simple harmonic motion with an amplitude of 10 cm and time period 6 s. At t = 0 it is at position x = 5 cm going towards positive x-direction. Write the equation for the displacement x at time t. Find the magnitude of the acceleration of the particle at t = 4 s.
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.
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 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
Describe Simple Harmonic Motion as a projection of uniform circular motion.
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 ______
