A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.8 m beyond its natural length and then released. If an external force of F(t) = 20eN is applied to the spring, find the position of the mass at any time t. x(t) =
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- A spring with natural length .5 m has length 50.5 cm with a mass of 2 gm suspended from it. The mass is initially displaced 1.5 cm below equilibrium and released with zero velocity. Find its displacement for t> 0. Note: Use g y(t) = 980 cm/s²A 0.500-kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 3.65 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm?Chapter 16: Problem 5: The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground. a) If the spring stretches x1 = 0.255 m from equilibrium while supporting an 7.6-kg child, what is its spring constant, in newtons per meter? b) What is the time, in seconds, for one complete bounce of this child about the point x1? c) What is the child’s maximum velocity, in meters per second, if the amplitude of her bounce, relative to x1, is 0.205 m?
- A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.6 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.) x(t) =Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to report the mass truthfully). (a)What is the force constant (in N/m) of the spring in such a scale if it stretches 7.70 cm for a 14.0 kg load? ____________ N/m (b)What is the mass (in kg) of a fish that stretches the spring 5.50 cm? ________________ kg (c) How far apart (in mm) are the half-kilogram marks on the scale? _____________mmA 0.500-kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 1.58 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm?