A120 g block attached to a spring with spring constant 2.0 N/m oscillates horizo

Question

A120 g block attached to a spring with spring constant 2.0 N/m oscillates horizontally on a frictionless table. Its velocity is 25 cm/s when x0 = -4.9 cm What is the amplitude of oscillation? Express your answer to two significant figures and include the appropriate units. What is the block's maximum acceleration? Express your answer to two significant figures and include the appropriate units.What is the block's position when the acceleration is maximum? Express your answer to two significant figures and include the appropriate units. What is the speed of the block when x1 =3.4 cm ? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given data

m = 120 g = 0.12 kg

k = 2 N/m

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

= sqrt(2/0.12)

= 4.08 rad/s

A) Apply energy conservation

0.5*k*A^2 = 0.5*k*x^2 + 0.5*m*v^2

A^2 = k*x^2/m + v^2

A^2 = w^2*x^2 + v^2

A = sqrt(w^2*x^2 + v^2)

= sqrt(4.08^2*0.049^2 + 0.25^2)

= 0.32 m or 32 cm

B) a_max = A*w^2

= 0.32*4.08^2

= 5.33 m/s^2

C) x = -A

= -0.32 m

D) Apply conservation of energy

0.5*k*A^2 = 0.5*k*x^2 + 0.5*m*v^2

0.5*m*v^2 = 0.5*k*A^2 - 0.5*k*x^2

v^2 = (k/m)*(A^2 - x^2)

v^2 = w^2*(A^2 -x^2)

v = w*sqrt(A^2 - x^2)

= 4.08*sqrt(0.32^2 - 0.034^2)

= 1.298 m/s

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