A punch-bag of mass 0.60 kg is struck so that it oscillates with SHM.  The oscillation has a frequency of 2.6 Hz and an amplitude of 0.45 m.  What is:

(a)    the maximum velocity of the bag;

(b)   the maximum kinetic energy of the bag?

(c)    What happens to the energy as the oscillations die away?                                  

(a) Formula first: v² = (2pf )²(A² – x²)

Maximum velocity occurs when the displacement is zero (P)

v² = (2 × p × 2.66 Hz)² × (0.45² m² – 0) (P)

   =  (16.71 Hz)² × 0.2025 m²

   = 56.5 m²/s²

v = 7.52 m/s  (P)

(b) Max Ek = ½ mv² = ½ × 0.6 kg × (7.52 m/s)²  (P)

= 17 J (P)

(c) It is transferred to the surroundings (P)

as heat. (P)