Question

PHYS 140-1 Test 5 November 20, 2019 Do all work in the examination book. 1. A block of mass 1.80 kg is suspended from an ideal spring with force constant k = 0.200 N/m. The mass is pushed 15.0 cm below its equilibrium position and then given an initial speed of 0.300 m/s directed downward (watch signs). a. What is the period of the resulting SHM of the block? Show work. (15 points) b. Taking the upward direction as a positive y-axis, the resulting motion of the block can be written as y = y, cos(01 + 0) (y in m, 1 in s). Find the values of o, y, and o. Show work. (15 points)

Answer 1

Seth (a) y=Ym Cos (wt+ Kx Here, a0-333 xad s y'e- Sin (cot F=-Kx ALL-0, y(o) - 0-15 m m- Eino, Soin wrti be 0sillahgy 0-15= Y cosd -i) So, Let A CWI Atto, y'lo 0.3 m Plugging in above esn; (fre) 0-3=m*0.333 Sm O-9=ym Sinp m 1212 Acos(2nt) --KAca n) T2 Drvidung esn-) by (u) tanp= 0. -6 KA = m (2n)2 A T2 2)2 m K -0-15 tant-- tan Bo.5u') =180-80.Sy = 99.46 T: 22. m 1-336ad T- 2 80 0-9 = 0.912 m 0.2 Sn a9.46) T-18.85 Ym=0.412 m w= 20 0.2 1-80 O.333 adls