The equation of damped oscillations is given in the form x=0.05e^-0.25sin½πt (m). Find the velocity of an oscillating point at the moments of time: 0, T, 2T, 3T and 4T.​

Explanation:

The logarithmic damping decrement of a mathematical pendulum is DeltaT=0.5. How will the amplitude of oscillations decrease during one full oscillation of the pendulum

Explanation:

ω = π/2 = 2π/T

T = 2π/(π/2) = 4 s

velocity is the derivative of position

v(t) = (-1/80)(e^(-t/4)[sin(πt/2) - 2πcos(πt/2)]

0T = v(0) = (-1/80)(e^(-0/4)[sin(π0/2) - 2πcos(π0/2)] = 0.078540

 T = v(4) = (-1/80)(e^(-4/4)[sin(π4/2) - 2πcos(π4/2)] = 0.028893

2T = v(8) = (-1/80)(e^(-8/4)[sin(π8/2) - 2πcos(π8/2)] = 0.010629

3T = v(12) = (-1/80)(e^(-12/4)[sin(π12/2) - 2πcos(π12/2)] = 0.003910

4T = v(16) = (-1/80)(e^(-16/4)[sin(π16/2) - 2πcos(π16/2)] = 0.001439