A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is

Question

x(t) = 8 sin t, where t is in seconds and x is in centimeters.

The first part of the question is to find the velocity and acceleration equations, which I got to be: v(t)=8cost and a(t)=-8sint.

Next, it asks: Find the position, velocity, and acceleration of the mass at time t = 2ð/3.

For v(t), I got -4, which is correct. For the x(t), I got 6.93, which is wrong, and a(t), I got -6.93, which is also wrong. What am I doing?

Answer 1

you v(t) and a(t) are both correct

sin 2π/3 = √3/2
cos 2π/3 = 1/2

so 8(√3/2) = 4√3 = appr 6.92820323 on my calculator
so it depends what accuracy is required

both of your answers are correct to two decimal places.