Part A Determine the amplitude. Part B Determine the period. In s Part C Determi

Question

Part A Determine the amplitude. Part B Determine the period. In s Part C Determine the spring constant. In N/m Part D Determine the maximum speed Part E Determine the total energy. In J Part F Please show work The position of a 52g oscillating mass is given by x(t)=2.0 cm cos 13t, where t is in seconds. Determine the amplitude. Determine the period. In s Determine the spring constant. In N/m Determine the maximum speed Determine the total energy. In J Determine the velocity at t t = 4.5 times 10?2s s . In m/s

Explanation / Answer

General form: x(t) = A cos (?t)

(1) Amplitude = A = 2.0cm

(2) Period = 2?/? = 2*3.14/13 = 0.483 seconds

(3) Spring constant can be found using: ? = 1/(2?) *?(k/m) where m is mass and k is spring constant

k = m?2 = 0.052 kg * 13 *13 * 2 * 3.14 = 55.18 N/m

(4) Velocity, v(t) = dx/dt = -A? sin(?t)

Maximum velocity = A? = 2.0cm * 13 = 26cm/s

(5) Total energy = 0.5 m?2 = 0.5 * 0.052kg * 13*13 = 4.394 joules

(6) Velocity at t = 0.45 sec:

v(t = 0.45) = - 2.0*13* sin (13*0.45) = +10.91 cm/s

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