Chapter 12: 2004 Set 11

A = 5.0 m

2pf = 0.40
f = 0.40/2p
f = 0.0637 hz

phase = 0.10 radians

x = 5.0 cos [0.40(2) + 0.10]
x = 3.11 m
(remember that your calculator must be in radians!]

#6  A body oscillates in SHM according to the equation: x = 8.0 cos (1.2t + 0.4)

A = 8.0 m

2pf = 1.2
f = 1.2/2p
f = 0.191 hz

T = 1 / f
T = 5.24 seconds

#8  Given: v = 1.57 m/sec; A = 0.5 mm = 0.0005 meters.  Set v = A(2pf) and solve for the frequency, f.

v= A(2pf)
1.57 = 0.0005 (2pf)
f = 1.57 / 0.0010p
f = 1.57 / 0.0010p
f = 500 hz

#17  Given: m = 0.20 grams = 0.0002 kg; f = 18 hz.  Use the equations T = 1 / f and  T = 2p (m/k) and solve for k.

1/18 = 2p (0.0002/k)
k = 2.56 N/m

#18 Given: m = 5 kg, k = 50 N/m, A = 10 cm = 0.10 m.  Use conservation of energy, PE_e = KE and solve for v.

KE = PE_e
½mv² = ½kA²
v = A (k / m)
v = 0.10  (50 / 5)
v = 0.316 m/sec

#22 At 5.0 cm, the energy is both KE and PEe.  By conservation of energy, PE_{e10 cm} = (KE + PE_e )_{5 cm}

PE_e = KE + PE_e
½(50)(0.10)² = ½(50)(0.05)² + ½(5)v²
0.25 = 0.0625 + 2.5v²
0.1875 = 2.5 v²
v = 0.274 m/sec