A mass of 5.0 kg slides down a friction less slope into a spring with spring constant k = 4.9 kN/m as depicted in Figure P11.65. 

(a) If the spring experiences a maximum compression of 20 cm, what is the height h of the initial release point? 

(b) What is the velocity of the mass when the spring has been compressed 15 cm? 

(c) If the mass sticks to the end of the spring, what are the period and amplitude of the oscillations that take place? 

(d) Determine the expressions for position as a function of time, x(t), and velocity as a function of time, v(t), for this oscillator. 

(e) What is the maximum velocity of the mass during any oscillation? 

(f) If the spring were to break while the mass is at the equilibrium position and moving to the right, to what maximum height would the mass rise up the slope? 

(g) Sketch or plot the position–time graph and velocity–time graph for the first second of the periodic motion.

Figure P11.65

 

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