# Vibration and energy

1. Vibration
2. Hooke's Law
3. Energy
##### Examples
###### Lessons
1. When a family of three with a total mass of 150kg steps into their 1100kg car, the car's spring compresses 2.0cm.
1. What is the spring constant of the car's spring?
2. How far will the car lower if loaded with 400kg?
2. A spring is 45cm long when a weight of 65N hangs from it but is 96cm when a weight of 190 N hangs from it. What is the spring constant?
1. A spring stretches 0.120m vertically when a mass of 0.400kg is attached to its end. Then spring is set up horizontally with the 0.400kg resting on a frictionless surface. The mass is pulled so that the spring is stretched 0.200m from the equilibrium position.
1. Find the spring constant
2. Find the amplitude of the horizontal oscillation
3. What is the magnitude of the maximum velocity?
4. Find the magnitude of the velocity when the mass is 0.04m from the equilibrium.
5. Determine the maximum acceleration of the mass.
2. An object with mass 4.0kg is attached to a spring with spring stiffness constant $k$ = 200N/m and is performing the simple harmonic motion. When the object is 0.04m from its equilibrium position, it is moving with a speed of 0.62m/s.
1. Calculate the amplitude of the motion.
2. Calculate the maximum velocity attained by the object.
3. A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 2.0J of work is required to compress the spring by 0.14m.

If the mass experiences a maximum acceleration of 18 m/s2;
1. Find the spring constant
2. Find the mass