Question

(15 pts) A 0.50 kg object connected to a spring with a spring constant of 350 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.00 cm. a) What is the angular frequency of the oscillation? b) What is the maximum speed of the object? c) At what position does this maximum speed occur? d) What is the acceleration of the object at x = 2.00 cm? e) What is the total energy of the mass-spring system?

Answer 1

given
mass , m = 0.50 kg
spring constant, k = 350 N/m
Amplitude, A = 4 cm = 0.04 m

a) angular frequency of motion, w = sqrt(k/m)

= sqrt(350/0.5)

= 26.4 rad/s <<<<<<<<----------Answer

b) maximum speed, v_max = A*w

= 0.04*26.4

= 1.06 m/s <<<<<<<<----------Answer

c) at mean position. i.e x = 0 cm

d) use, F = -k*x

m*a = -k*x

a = -k*x/m

= -350*0.02/0.5

= -14.0 m/s^2 <<<<------Answer

here negative sign indicates -x direction.
If only magnitude if needed, |a| = 14.0 m/s^2

e) Total energy of the system = (1/2)*k*A^2

= (1/2)*350*0.04^2

= 0.280 J <<<<------Answer