P13

         k = 25 N/cm = 2500 N/m,      V = 1.5 m/s

       (1/2) mV**2 = (1/2) kx**2      x**2 = (m/k) V**2 = (2/2500) x 1.5**2 = 0.0018

                 x = 0.042 m = 4.2 cm

P51

                  f = 78 rpm = 78/60 rps = 1.3 Hz

                 w = 2pf = 8.06 rad/s

P57

               (a)  A = 5 m

               (b) w = 0.4 rad

               (c)  initial phase = 0.1 rad

               (d) x = 5 cos (0.4x 2 + 0.1) = 5 cos(0.9 rad) = 3.1 m

P69

              m = 0.2 g = 2 x 10**-4 kg       f = 18 Hz = (k/m)**0.5 / 2p

              k = m (2p f)**2 = 2 x 10 **-4 x (2p f)**2 = 2.55 N/m

P85

              L = 10 m f = (g/L)**0.5 / (2p) = 0.158 Hz