17. Periodic Motion
Energy in Simple Harmonic Motion
2PRACTICE PROBLEM
A spring-mass system is used to simulate the motion of the human hamstring. The hamstring executes a simple harmonic with an amplitude of 15 cm and an angular frequency of 6.28 rad/s. Calculate I) i) the maximum magnitude of the acceleration and ii) the speed at the equilibrium position; II) i) the acceleration and ii) speed at the position x=-7.5 cm; III) the time needed to go directly from x=0 cm to x=+7.5 cm IV) Which of the quantities requested previously can be determined using the conservation of mechanical energy?
A spring-mass system is used to simulate the motion of the human hamstring. The hamstring executes a simple harmonic with an amplitude of 15 cm and an angular frequency of 6.28 rad/s. Calculate I) i) the maximum magnitude of the acceleration and ii) the speed at the equilibrium position; II) i) the acceleration and ii) speed at the position x=-7.5 cm; III) the time needed to go directly from x=0 cm to x=+7.5 cm IV) Which of the quantities requested previously can be determined using the conservation of mechanical energy?
ANSWERS OPTIONS
A
I) i) ax,max=5.9 m/s2 II) i) vmax=0.94 m/s
II) ax=2.96 m/s2 ii) v=0.82 m/s
III) 0.08 s
IV) speed and acceleration
II) ax=2.96 m/s2 ii) v=0.82 m/s
III) 0.08 s
IV) speed and acceleration
B
I) i) ax,max=5.9 m/s2 II) i) vmax=1.94 m/s
II) ax=2.96 m/s2 ii) v=1.82 m/s
III) 0.08 s
IV) speed and acceleration
II) ax=2.96 m/s2 ii) v=1.82 m/s
III) 0.08 s
IV) speed and acceleration
C
I) i) ax,max=3.9 m/s2 II) i) vmax=0.94 m/s
II) ax=1.95 m/s2 ii) v=0.82 m/s
III) 0.18 s
IV) time and acceleration
II) ax=1.95 m/s2 ii) v=0.82 m/s
III) 0.18 s
IV) time and acceleration
D
I) i) ax,max=5.9 m/s2 II) i) vmax=0.94 m/s
II) ax=2.96 m/s2 ii) v=0.82 m/s
III) 0.18 s
IV) time and acceleration
II) ax=2.96 m/s2 ii) v=0.82 m/s
III) 0.18 s
IV) time and acceleration