Question

A block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 10.0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 27.0 cm/s.

(a) Calculate the mass of the block.

(b) Calculate the period of the motion.

(c) Calculate the maximum acceleration of the block.

Answer 1

Spring constant k = 5.5 N/m

Amplitude A = 10 cm = 0.1 m

Speed of the block is halfway between its equilibrium position and the end point v = 27 cm / s = 0.27 m/s

we know v = w [A ² - X ² ] Given displacment X = A/2

0.27 = w [A ² - (A/2) ² ]

= w [(3)]A/ 2

From this w = 2(0.27) / A3

= 3.117 rad/s Since A = 0.1 m

We know k = mw ²

From this mass m = k/w ²

= 5.5 /(3.117) ²

= 0.565 kg

(b).Period T = 2(pi) / w

= (2x3.1415) / 3.117

= 2.015 s

(c).maximum acceleration a = Aw²

a = 0.1 (3.117) ²

= 0.971 m/s ²