A 300 g mass vibrates according to the equation x = 0.38 sin 6.50t, where x is in metes nad t is in seconds.?

Question

Determine (a) the amplitude, frequency, the period, the total energy, and the KE and PE when x is 9.0 cm?

Answer 1

x = Xsin(2πft)
X = 0.38
f = 6.50/(2π) ≈ 1.0345 Hz
v = 2.47cos(6.50t)
E = (1/2)300(2.47)^2 = 915.135 J

@ x = 9 cm
0.09 = 0.38 sin 6.50t
sin 6.50t1 = 0.09/0.38 = 0.23684
cos 6.50t1 = (1 - 0.23684^2)^(1/2) = 0.97155
v1 = 2.47(0.97155) = 2.3997
KE1 = (1/2)(300)(2.3997)^2 = 863.80125 J
PE1 = 915.135 - 863.80125 = 51.33375 J