A body oscillates with SHM according to the equation (in SI units), x = 10 cos[4πt + π/2]. At t = 0.5 s, calculate the (a) Displacement (b) Speed (c) Acceleration of the body.

In simple harmonic motion (SHM), the displacement x(t) of a particle from its equilibrium position is given by:

x(t) = A cos(ωt + φ)

where A is the amplitude of the displacement, (ωt + φ) is the phase of the motion, and φ is the phase constant.

Given: A = 10, ω = 4π, φ = π/2

Time period T = ^2π/_ω = ^2π/_4π = 0.5 s

At t = 0.5 s:

(a) Displacement = 10 cos[4π(0.5) + π/2] = 10 cos[2π + π/2] = 0 m

(b) Speed = -ωA sin(ωt + φ) = -(4π)(10) sin(2π + π/2) = -40π m/s

(c) Acceleration a(t) = -ω²A cos(ωt + φ) = -ω²x(t)

∴ a(t) = -(4π)²(10) cos(2π + π/2) = 0 m/s²