A 1.50-kg mass on a spring has displacement as a function of time given by x(t) = (7.40 cm) cos [(4.16 rad/s)t - 2.42] Find (a) the time for one complete vibration; (b) the force constant of the spring; (c) the maximum speed of the mass; (d) the maxi-mum force on the mass; (e) the position, speed, and acceleration of the mass at t = 1.00 s; (f) the force on the mass at that time.

Solution 19E Step 1 of 6: a) Time period , T = = 4.16 rad/s1.51 s Step 2 of 6: k b)we have relation , = m Force constant ,k = m = 1.5 kg × (4.16 rad/s) = 26 N/m Step 3 of 6: c)Maximum speed ,v = A = 4.16 rad/s × 7.4 cm = 30.8 cm/s max