Originally Posted by

**afeasfaerw23231233** bk2 p90 q24 c d

i don't know how to do c) and d)

question: The displacement x at time t of a particle is given by

x = A sin 2t + B cos 2t

where A and B are constants.

a) if x satisfies the equation

$\displaystyle \frac {d^2 x }{dt^2} + 3 \frac {dx}{dt} - 4x = sin 2t $

find the values of A and B

b) What is the max. displacement of the particle?

c) show that the speed at time t is given by $\displaystyle 2 \sqrt {A^2 +B^2 - x^2}$

d) hence find the maximum speed of the particle

my working:

dx/dt = 2A cos 2t - 2B sin 2t

$\displaystyle \frac {d^2 x }{dt^2} = -4A sin 2t - 4B cos 2t$

A = -2/25

B = -3/50

when dx/dt = 0

tan 2t = 4/3

sin 2t = 4/5 or -4/5

cos 2t = 3/5 or -3/5

max. of x = 1/10

don't know how to do c) and d) . thanks