Advertisements
Advertisements
Question
A particle performs linear S.H.M. of period 4 seconds and amplitude 4 cm. Find the time taken by it to travel a distance of 1 cm from the positive extreme position.
Advertisements
Solution
Given:
T = 4 s, A = 4 cm = 0.04 m,
x = 1 cm from extreme position = 4 − 1 = 3 cm = 0.03 m
To find: Time taken (t)
Formula: x = A sin (ωt + Φ)
Calculation:
Particle starts from a positive extreme position.
∴ Φ = `pi/2`
From formula,
x = `"A" sin((2pi"t")/"T" + Φ)` ........`(∵ ω = (2pi)/"T")`
∴ 3 = 4 sin`((2pi"t")/4 + pi/2)`
∴ cos`((2pi)/4)"t" = 3/4` ......`[∵ sin(pi/2 + θ) = cosθ]`
∴ `(pi/2)"t" = cos^-1(3/4)`
∴ t = `2/pi xx 41.1^circ xx pi/180 = 41.4/90 = 0.46 "s"`
Time taken by it to travel a distance of 1 cm from the positive extreme position is 0.46 s.
APPEARS IN
RELATED QUESTIONS
At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 8 cm, three times its potential energy?
A simple pendulum moves from one end to the other in ¼ second. What is its frequency?
What is the amplitude of S.H.M.
The acceleration due to gravity on the surface of the moon is 1.7 m/s2. What is the time period of a simple pendulum on the surface of the moon if its time period on the surface of the earth is 3.5 s? (g on the surface of earth = 9.8 m/s2)
A particle performing S.H.M. has velocities of 8 cm/s and 6 cm/s at displacements of 3 cm and 4 cm respectively. Calculate the amplitude and period of S.H.M.
In amplitude modulation,
The total energy of the body executing S.H.M. is E. The kinetic energy of the body, when the displacement is half of the amplitude is ______.
When a mass is hung from a light spring, the spring extends by 10 cm. If the mass is pulled down and let go, it executes S.H.M. with a time period (g = 10 m/s2) ____________.
If 'x', 'v' and 'a' denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time t, then which one of the following does not change with time?
Three masses 700 g, 500 g, and 400 g are suspended at the end of a spring and are in equilibrium as shown in figure. When the 700 g mass is removed, the system oscillates with a period of 3 seconds; when the 500 g mass is also removed, it will oscillate with a period of ____________.
The equation of S.H.M. of a particle of amplitude 4 cm performing 150 oscillations per minute starting with an initial phase 30° is ____________.
A body of mass 1 kg is suspended from a spring of negligible mass. Another body of mass 500 g moving vertically upwards hits the suspended body with a velocity 3 ms-1 and gets embedded in it. If the frequency of oscillation of the system of the two bodies after collision `10/pi` Hz, the amplitude of motion and the spring constant are respectively ____________.
A horizontal spring executes S.H.M. with amplitude 'A1', when mass 'm1' is attached to it, When it passes through mean position another mass 'm2' is placed on it. Both masses move together with amplitude 'A2'. Therefore A2 : A1 is ______
A mass M attached to a horizontal spring executes S.H.M. of amplitude A1. When the mass M passes through its mean position, then a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of `(A_1/A_2)` is ______
A mass is suspended from a vertical spring which is executing S.H.M. of frequency 5 Hz. The spring is unstretched at the highest point of oscillation. Maximum speed of the mass is ______. [acceleration due to gravity g = 10 m/s2]
A particle performing SHM starts equilibrium position and its time period is 16 seconds. After 2 seconds its velocity is π m/s. Amplitude of oscillation is ______. `(cos 45° = 1/sqrt2)`
A block of mass m, connected to two springs of spring constants k1 and k2 as shown, oscillates on a smooth horizontal surface. What is the effective spring constant of the oscillation?
A particle performs linear SHM with amplitude A and frequency n. Its speed midway between an extreme position and equilibrium position is ______.
Light of a certain colour has 2500 waves to the millimetre in air. What is its frequency?
