10-30. A block of mass m is dropped from a height h above a spring k,...

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10-30. A block of mass m is dropped from a height h above a spring k, as shown in Fig. P10.30. Beginning at the time of impact (t = 0), the position x(t) of the block satisfies the following second-order differential equation and initial conditions: m¨x(t) + k x(t) = m g, x(0)=0, x(0) = √2gh. a. Determine the transient solution Xtran(t), and determine the frequency of oscillation. b. Determine the steady-state solution xsg(t). Figure P10.30 Mass dropped on a spring. c. Determine the total solution x(t), subject to the initial conditions. d. Mark each of the following statements as true (T) or false (F): Increasing the stiffness k will increase the frequency of x(t). Increasing the height h will increase the frequency of x(t). Increasing the mass m will decrease the frequency of x(t). Doubling the height h will double the maximum value of x(t). Doubling the mass m will double the maximum value of x(t). g m momo k x(t) -t=0 10-30. A block of mass m is dropped from a height h above a spring k, as shown in Fig. P10.30. Beginning at the time of impact (t = 0), the position x(t) of the block satisfies the following second-order differential equation and initial conditions: m¨x(t) + k x(t) = m g, x(0)=0, x(0) = √2gh. a. Determine the transient solution Xtran(t), and determine the frequency of oscillation. b. Determine the steady-state solution xsg(t). Figure P10.30 Mass dropped on a spring. c. Determine the total solution x(t), subject to the initial conditions. d. Mark each of the following statements as true (T) or false (F): Increasing the stiffness k will increase the frequency of x(t). Increasing the height h will increase the frequency of x(t). Increasing the mass m will decrease the frequency of x(t). Doubling the height h will double the maximum value of x(t). Doubling the mass m will double the maximum value of x(t). g m momo k x(t) -t=0

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