Q4. 1) Consider a mass m attached to a vertical real spring of stiffness k and natural length a. The spring is denoted S

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Q4 1 Consider A Mass M Attached To A Vertical Real Spring Of Stiffness K And Natural Length A The Spring Is Denoted S 1 (50.52 KiB) Viewed 13 times

Q4. 1) Consider a mass m attached to a vertical real spring of stiffness k and natural length a. The spring is denoted S(k, a, C) in the picture below: on the left is the equilibrium position denoted by X, and on the right is the mass in motion with a displacement r(t). C is the damping coefficient. The mass is moving along the vertical direction without friction Sik, a, C) Sk. a. C) X1 (t) (5) Find the equilibrium position X (b) Using Newton's second law, derive the differential equation satisfied by the displace ment (0) Assuming that C - Amk < 0, solve for z(t) considering that the spring is extended by , at t = 0 and released from rest. [10 marks] 2) Consider the mass m attached to two identical ideal springs defined as $(k, a) as depicted in the figure below. The system is moving horizontally without friction. Sika) mmmmmm 0000000000000 S( ka) Consider that when in motion, the mass m has an extension r(t) (positive to the right) (2) Using the Newton's second law, derive the equation of motion satisfied by the mass in motion (b) Solve for () by considering that initially, the mass is extended by 30 (positive) from rest [10 marks] [Total: 20 marks]