Question

A spring-mass system (spring constant 80N/m and damping coefficient 40N-s/m), initially at rest, is lying along the y-axis in the horizontal plane. One end of the spring is fixed and the mass (5kg) is attached at its other end. The mass is pulled along the y-axis by 0.5m from its equilibrium position and then released. Choose the correct statement(s).
(Ignore mass of the spring)

• A. Motion will be under damped
• B. Trajectory of the mass will be 𝑦(𝑡) = $\frac{1 }{2} (1 + 𝑡)𝑒^{-4t}$
• C. Motion will be critically damped
• D. Trajectory of the mass will be 𝑦(𝑡) = $\frac{1 }{2} (1 + 4𝑡)𝑒^{-4t}$

Answer 1

Answer: (C), (D)

Motion will be critically damped

Answer 2

The correct options are: C and D