How do you find the amplitude and period of #y=3sin(2t)#?

1 Answer
Nikhil F.
Nov 26, 2016

Amplitude: 3
Period: #pi#

Explanation:

graph{y=3sin(2x) [-5.46, 14.54, -4.28, 5.72]}

Considering the #x#-axis to be the time as the wave progresses and the #y#-axis the displacement, the period can be seen to be #pi# as that is the time taken for one complete oscillation

(Proof)

#y=0#

#0=3sin(2t)#

#0=sin(2t)#

#2t=sin^-1(0)#

#2t=0,pi,2pi,3pi,4pi ...#

#t=0,1/2pi,pi,3/2pi,2pi ...#

(every second time the wave crosses the #x#-axis is a complete oscillation)

#t=0,pi,2pi ...#

The constant difference is #pi#
#therefore# the period is #pi#

The amplitude is the maximum distance from the rest point of a wave - this is the same as the maximum value of the graph.

#y=sinx# has a range of #-1<=y<=1#
(the maximum value possible is 1)

This makes the maximum value of #3sin(2t) = 3(1) =3#
#therefore# the amplitude is 3

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