Question

A body oscillates with SHM accaording to the the equation x=6sin(20t + π/4). Then its maximum acceleration of the body?

Answer 1

Answer:

Given:

Equation of SHM :

x = 6 sin(20t + π/4)

To find:

Max acceleration of the body.

Concept:

An oscillating body experiences max acceleration at the amplitude position when the velocity becomes zero.

Calculation:

Comparing the given Equation with a standard Equation of SHM

x = A sin(ωt + θ)

we get , A = 6 , ω =20 , θ = π/4.

So max acceleration is given as follows:

Acc. (max) = - ω²A

=> Acc. (max) = - (20)² × 6

=> Acc (max) = -2400 m/s²

Negative sign denotes opposite direction of acceleration wrt. displacement.

Here , I have considered all units in SI.

So final answer is -2400 m/s².

Answer 2

Answer:

x= 6 sin(20t + Π/4

acceleration = d^x /dt^2 that is it is double derivative of displacement

dx/dt = 6 (20)cos(20t +Π/4)

= 120 cos(20t + Π/4)

Now again differentiate

Now d( dx/dt)/dt

= - 120 (20) sin(20t + Π/4)

= -2400 sin( 20t + Π/4)

Obviously minus sign denotes opp.direction with displacement

For max acceleration

take sin (20t +Π/4) = 1 as max value of sin is 1

So, Max acceleration = -2400