Question

1. A simple pendulum makes 39 oscillations in 51 seconds. 2228 NOTES IMAGES DISCUSS UNITS STATS HELP PREFERENCES Part Description Answer Save Determine the period of the pendulum. (include units with answer) 11 pts. 110% Format Check 2% try penalty Hints: 0,0 11 pts. 110% Determine the length of the I pendulum. Assume small angle oscillatons. (include units with answer) Format Check 2% try penalty Hints: 0,0 11 pts. 110% c. At t=0, the pendulum is released from rest at an angle of +6 degrees. Determine the angle at t = 5.3 seconds. (include units with answer) Format Check 2% try penalty Hints: 0,0 11 pts. 110% D. If the pendulum is released from rest at an angle of 45 degrees, what is the period of oscillation? (include units with answer) Format Check 2% try penalty Hints: 0,0

Answer 1

- some simple pendulum makes 39 osciliation in Sl seconds 39 Oscillatim in si seconds I oscillations in = SI = 1.3077 See. So period of oscillation, T = 1.3077 see. 6 time perod of oscillation is giren by (for small period) T= are = 1:3077 (g = 981 m/s2) e = 0.4249m © General egn for angle o at any time t - I V _- - - - ng sino)L= I (do) (I= ME) ME( 80 ) + ing sing) = 0 do + (8) sino = 0 for small peniod, O small = 60 (small Sino0 angle)

d42 1.3077 o(t) = 0. Cos (WA) t=0, 0 =, W = 8 t = I1 = 4.804 radl sec. Period 0(t) = 0o Cop (4.804 +) t=0, 0o=60, 6 = 0o OCD) - (6963(4.804t) t-a5.3 sec. = Olt)= 60 Cos (4.804 853) To(t) = 5.678°/ ® If angle is large, then time perioda) do +69 )sino - 0 By solving this, we get time period T= 20 57 [1 + 1 6 8 + 11 + - ]{0o =) - 21/0 4295 [1+ Te (4) + 22 (4)*-] IT= 1.35989 sec. I time period d+2 9.81