An object-spring system oscillates with an amplitude of 2.8 cm. If the spring constant is 200 N/m and object?

m = mass of the object = 0.5 kg

k = spring constant = 200 N/m

A = amplitude = 0.028 m

The mechanical energy in the system can be found by:

ME = k × A² / 2

ME = (200 N/m) × (0.028 m)² / 2

ME = 0.0784 J < - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - answer

The maximum speed occurs when all energy is converted to kinetic energy, so

ME = KE = m × V² / 2

or

V = √( 2 × ME / m)

V = √( 2 × (0.0784 J) / (0.5 kg) )

V = 0.56 m/s < - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - answer

The maximum acceleration can be found by:

a = k × A / m

a = (200 N/m) × (0.028 m) / (0.5 kg)

a = 11.2 m/s² < - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - answer

y = A*sin*(sqrt(ok/m)*t) via definition: v = sqrt(ok/m)*A*cos(sqrt(ok/m)*t) a = -ok/m*A*sin(sqrt(ok/m)*t) optimal velocity happens while the cos term is a million or -a million v_max = sqrt(ok/m)*A = sqrt(251 N/m / .432 kg) * .0.5 m = .844 m/s optimal acceleration happens while the sin term is a million or -a million a = -ok/m*A = 251 N/m / .432 kg * .0.5 m = 20.3 m/s^2 **** have my m/ok backwards... Steve became into actual along with his...