Question

18) A package is oscillating on a spring scale with a period of 4. 60 s. At time t = 0. 00 s the package has zero speed and is at x = 8. 30 cm. At what time after t = 0. 00 s will the package first be at x = 4. 15 cm? A) 0. 575 s B) 0. 767 s C) 1. 15 s D) 1. 30 s E) 1. 53 s

Answer 1

B) is correct

x = A cos ω t satisfies the conditions with max amplitude at t = 0 and zero velocity

P = 1/f = 2 π / ω

ω = 2 π / 4.60 = 1.36 angular frequency

x = 4.15 = 8.30 cos ω t

cos ω t = .500

ω t = 60 deg = 360 / 6 = 2 π / 6 = 1.05 rad

t = 1.05 / 1.36 = .772 sec