A simple harmonic motion is represented by $x = 10 sin (20 t + 0.5)$ .
Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time in second.

Open in App

Solution

$x = 10 sin (20 t + 0.5) . . . . . (1)$
Equation of SHM
$x = A sin (ω t + ϕ) . . . . . (2)$
$A = a m p l i t u d e$
$ω =$ angular frequency
$ϕ =$ initial phase
Comparing coefficients of $(1)$ and $(2)$
$A = 10 m$
$ω = 20 r a d s^{- 1}$
$ϕ = 0.5 r a d$
$ω = 2 π f$
$f = \frac{ω}{2 π} = \frac{20}{2 \times 3.14} = 3.18 H z$
$T = \frac{2 π}{ω} = 2 π \frac{2 \times 3.14}{20} = 0.314 s$ .

Suggest Corrections

Similar questions

Q. The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (ωt + ∅ ). If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is p s–1. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

Q. The displacement of a particle executing simple harmonic motion is given by equation y=0.3 sin 20

π

(t+0.05) where time t is in second and displacement y is in metre. calculate the values of amplitude, time period initial phase and initial displacement of the particle .

Q. A particle executing simple harmonic motion has an angular frequency of

6.28 s^{- 1}

and amplitude of

10 c m

. The time period of the SHM is :

Q. The displacement x (in metres) of a particle is simple harmonic motion is related to time t (in seconds) as x =

0.01 c o s (π t + \frac{π}{4})

What is the frequency of the motion?

A particle executes simple harmonic motion about the point X =0 . At time t =0 it has displacement cm and zero velocity. If the frequency of motion is $0.25 s e c^{- 2}$ , find
(a) the time period,
(b) angular frequency,
(c) the amplitude,
(d) maximum speed,
(e) the displacement at t =3 sec and
(f) the velocity at t =3 sec.

Join BYJU'S Learning Program

A simple harmonic motion is represented by x=10sin(20t+0.5).Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time in second.

x=10sin(20t+0.5).....(1)Equation of SHMx=Asin(ωt+ϕ).....(2)A=amplitudeω= angular frequencyϕ= initial phaseComparing coefficients of (1) and (2)A=10 mω=20 rad s−1ϕ=0.5 radω=2πff=ω2π=202×3.14=3.18 HzT=2πω=2π2×3.1420=0.314 s.

A simple harmonic motion is represented by $x = 10 sin (20 t + 0.5)$ .
Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metres and time in second.