Answer to Question #130484 in Physics for LimJW

Question

A particle of mass 5.0 kg moves in simple harmonic motion of amplitude 18 cm. It completes 20 oscillations in 4.0 s.

a. Determine the angular frequency of this SHM.

b. If at time t=0, the particle is at its maximum positive displacement, write the expression for the displacement x in terms of time t for this motion.

c. Find the displacement of the particle when i. t = 0.05 sii. t = 0.12 s iii. t = 0.18 s

d. Calculate the maximum velocity and maximum acceleration for this SHM.

e. Determine the total energy for the system.

Answer 1

a)

$$\omega=2\pi\frac{20}{4}=31.4\frac{rad}{s}$$

b)

$$x=0.18\cos{10\pi t}$$

c)

$$i)\ x=18\cos{10\pi (0.05)}=0\ cm\\ii)\ x=18\cos{10\pi (0.12)}=-14.6\ cm\\iii)\ x=18\cos{10\pi (0.18)}=14.6\ cm\\$$

d)

$$v=10\pi(0.18)=5.65\frac{m}{s}\\a=(10\pi)^2(0.18)=178\frac{m}{s^2}$$

e)

$$K=0.5(5)(5.65)^2=79.8\ J$$