Question

If y=0.4 sin (90t + 0.40) find the amplitude and angular frequency.

Answer 1

$\bigstar$ Answer $\bigstar$

$\checkmark$ Given:

$\blue{\implies \sf y =0.4 \;sin(90\; t+0.40)}$

$\checkmark$ To Find:

$\red{\sf \implies Amplitude \;(\;A\;)}$

$\red{\sf \implies Angular \ Frequency \; (\; \omega\;)}$

$\checkmark$ Solution:

We know that,

Generally,

$\green{\boxed{\boxed{\sf y =A \;sin(\omega \; t+\phi)}}}$

Where,

$\pink{\implies \sf A=Amplitude}$

$\purple{\sf \implies \omega = Angular \ Frequency}$

$\orange{\sf \implies \phi=Initial \ Phase}$

Given that

$\blue{\implies \sf y =0.4 \;sin(90\; t+0.40)}$

Therefore,

On Comparing the Given Equation to the General Equation

We get,

$\red{\sf \implies \underline{Amplitude} \;(\;A\;)}$

$\pink{\implies \sf A=0.4 \ m}$

$\red{\sf \implies \underline{Angular \ Frequency} \; (\; \omega\;)}$

$\purple{\sf \implies \omega = 90 \ rad/s}$

Hence,

$\orange{\sf \implies Amplitude \;(\;A\;)=0.4 \ m}$

$\pink{\sf \implies Angular \ Frequency \; (\; \omega\;)=90 \ rad/s}$

Answer 2

Answer :

y = A sin ( cos ωt + Ф )

where ,

A = Amplitude

ω = Angular Frequency

t = time

Ф = Initial Phase

Now  compare y=0.4 sin (90t + 0.40) with y = A sin ( cos ωt + Ф ) , we get ,

• Amplitude , A = 0.4 m

• ω = 90 rad/s