Question

A simple harmonic moving object with the equation of deviation y = 2 sin 1/12 π t, with y in meters and t in second. Compute:
A) amplitude
B) frequency
C) period
D) y within 2 seconds

Answer 1

general equation of SIMPLE HARMONIC motion is y = Asinwt

where A = amplitude
w = anguar frequency

we also know ,
w = 2π/T

where T is time period

now ,
compare y = Asinwt and y = 2sin1/12πt
A = 2
w = π/12

(a) amplitude = 2 metre

(b) frequency :-

2π/T = π/12

T = 24 sec

frequency = 1/T = 1/24 Hz


(c) Time peoid = 24sec

(d) y = 2sin1/12πt

t = 2 Sec

y = 2sin( 1/12π ×2)

2sin(π/6) = 2× 1/2 = 1 metre

Answer 2

Answer:-

General equation of SIMPLE HARMONIC motion is y = Asinwt

where A = amplitude

w = anguar frequency

we also know ,

w = 2π/T

where T is time period

now ,

compare y = Asinwt and y = 2sin1/12πt

A = 2

w = π/12

(a) amplitude = 2 metre

(b) frequency :-

2π/T = π/12

T = 24 sec

frequency = 1/T = 1/24 Hz

(c) Time peoid = 24sec

(d) y = 2sin1/12πt

t = 2 Sec

y = 2sin( 1/12π ×2)

2sin(π/6) = 2× 1/2 = 1 metre

hope it helps