Suppose a 32-pound weight is suspended on a spring.The weight is pulled foot below the equilibrium position and released.Assume that the weight stretches the spring foot from
Its natural position.Find a formula for the position of the weight as a function of time t.

Question

Suppose a 32-pound weight is suspended on a spring.The weight is pulled  foot below the equilibrium position and released.Assume that the weight stretches the spring  foot from
Its natural position.Find a formula for the position of the weight as a function of time t.

Quizplus · Accepted Answer

The position of the weight as a function of time t can be modeled by the equation:

y(t) = A*cos(wt) + B*sin(wt) + C

where A, B, and C are constants determined by the initial conditions, and w is the angular frequency of the motion given by:

w = sqrt(k/m)

where k is the spring constant and m is the mass of the weight.

Since the weight stretches the spring 11ebbd4d_3f18_991d_8a0a_5939969bc0c3_TB8202_11 foot from its natural position, we have:

C = 11ebbd4d_3f18_991d_8a0a_5939969bc0c3_TB8202_11

Since the weight is pulled 11ebbd4d_3f18_991c_8a0a_dfd199b824ea_TB8202_11 foot below the equilibrium position and released, we have:

y(0) = -11ebbd4d_3f18_991c_8a0a_dfd199b824ea_TB8202_11
y'(0) = 0

Taking the derivatives of the equation and using the initial conditions, we get:

y(t) = -11ebbd4d_3f18_9920_8a0a_4d40c3b072a1_TB8202_11*cos(wt) - 11ebbd4d_3f18_991e_8a0a_d9be9cc0965e_TB8202_11*sin(wt) + 11ebbd4d_3f18_991d_8a0a_5939969bc0c3_TB8202_11

Simplifying this equation, we get:

y(t) = 11ebbd4d_3f18_9922_8a0a_a5e2772cbbba_TB8202_11*cos(wt + 1.8875) + 11ebbd4d_3f18_991d_8a0a_5939969bc0c3_TB8202_11

Therefore, the answer is C.

Suppose a 32-Pound Weight Is Suspended on a Spring