A block of mass m hangs from a spring with a spring constant k. The block is initially held so that the spring is unstretched. If the natural circular frequency of the system is 10 radians/sec, how many cycles of vibration will the block experience in five seconds after it is released?

Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?

5. Two mass placed on top of each other have a mass of 20 g each and there is a coefficient of static friction equal to 0.60. The bottom mass is attached to spring with spring constant 10 N/m which is connected to a wall. The friction between the bottom mass and the floor is zero, What is the maximum amplitude of the oscillations before the top block slides off the bottom block? 20 g K = 10 N/m µ = 0.60 20 g el µ = 0

vibrating body with viscous damping makes 10 complete oscillations per second, and in 50 cycles diminishes to 20 percent. Determine the damped natural frequency, logarithmic decrement and the damping ratio.