Question

x=Asin wt+Bcos wt .executing SHM
what is its amplitude​

Answer 1

Answer:

Concept:

Amplitude refers to the maximum displacement of a particle performing oscillatory motion.

So we have to find out the max value of "x".

Given :

Equation of motion

x = A sin(wt) + B cos(wt)

Calculation:

A sin(wt) + B cos(wt)

= (√A² + B²) × [{A/(√A² +B²)} × sin(wt) + {B/(√A² +B²)} × cos(wt)]

[ let {A/(√A² +B²)} be cos θ,

then {B/(√A² +B²)} is sin θ.]

=(√A² + B²) [cos(θ) sin (wt) + sin (θ) cos(wt)]

=(√A² + B²) [sin (wt + θ)]

So maximum value for sin (wt + θ) is 1 .

So amplitude or max value of x

= (√A² + B²)

Answer 2

Answer:

Amplitude is the maximum displacement from its original position to its final position