Round to two decimal places if necessary. A spring is stretched 5 centimeters by a 15 N weight. The weight is then pulled down an additional 8 centimeters and released. Neglect damping. Find the function u(t) for the position of the spring at any time t. u(t) =

In this limit, what is the effective spring constant k for the pendulum in the limit of small angles? In this limit, what is the effective angular frequency ω of a pendulum in the limit of small angles?

A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur.  Answers: 0.01875 J, 0.01875 J

A 5 kg mass is hung on a spring with a stiffness of 70 N/m. Find the oscillation response of this mass as a function of time, if x0= 1 m and v0= - 0.45 m/s. x0 is the initial displacement and vo the initial speed. x = cos (3.74 t) - 0.12 sin(3.74 t) x = cos (14 t) - 0.12 sin(14 t) x = - 0.12 cos (3.74 t) + sin(3.74 t) x = - 0.12 sin(3.74 t) + cos (14 t)

A simple harmonic oscillator consists of a mass m attached to a spring with spring constant k, with displacement given by x = A sin(wt + ¢) . Which one of the following is NOT true? O The frequency is independent of the amplitude O The potential energy is a maximum when (wt + 4) = 0 The kinetic energy is a maximum when (wt + ¢) = 0 O The restoring force must be proportional to the negative of the displacement O Increasing the mass will decrease the frequency