Question

The acceleration of a particle at time t is given be a=-aw^2 sinwt. It's displacement at time t is

Answer 1

check the formulas once. the process is right . first integrate acc. to find velocity and then integrate velocity to find displacement.

hope it helps
the mechanic
tony

Answer 2

The displacement of the particle at time t is $a \sin wt$

Given : The acceleration of the particle at time t is given by a(t)  = $-aw^{2}\sin wt$

To Find : The displacement of the particle at time t

Solution : The displacement of the particle at time t is $a \sin wt$

Now we now that acceleration is rate of change of velocity of the particle

i.c

a = $a = \frac{dv}{dt}$

where v is the velocity of the particle

and velocity is rate of change of displacement which is given by

$v = \frac{dx}{dt}$

where x is the displacement

now

since acceleration a(t) is given as  $-aw^{2}\sin wt$

so $\frac{dv}{dt}$  = $-aw^{2}\sin wt$

v(t) = $\int_0^t -aw^{2}\sin wt$

v(t) = $aw\cos wt$

Now

v(t) = $\frac{dx}{dt}$

$\frac{dx}{dt}$ = $aw\cos wt$

x(t) = $\int_0^t aw\cos wt$

x(t) = $a \sin wt$

The displacement of the particle at time t is $a \sin wt$

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