Question

How is maximum acceleration=Aw2​

Answer 1

Answer:

let solve with a eg:

y=2sin[2πt+ϕ], where 2 is in cm

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)⇒A=2 cm,w=2π

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)⇒A=2 cm,w=2πAcceleration of the particle is 

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)⇒A=2 cm,w=2πAcceleration of the particle is a=w2x

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)⇒A=2 cm,w=2πAcceleration of the particle is a=w2xAt x=+A,a=amax

y=2sin[2πt+ϕ], where 2 is in cmCompare the equation with the standard equation,A=sin(wt+ϕ)⇒A=2 cm,w=2πAcceleration of the particle is a=w2xAt x=+A,a=amax∴amax=w2A=2π2 cm/s2