I am having trouble with the type of question listed below and any help would be greatly appreciated. I have attached a diagram also.

A block P of mass m is attached to three springs whose other ends are attached to fixed points A, B and C. I have listed the stiffnesses of the three springs and their natural lengths below. The point B is a distance 5L below A, and the point C is a distance 1/2L above B.

Spring = AP, Stiffness = 2k, Natural length = L
Spring = BP, Stiffness = 8k, Natural length = 1/2L
Spring = CP, Stiffness = 6k, Natural length = 3/2L

What should the datum for gravitational potential energy of particle P be? Why choose this point?
What is the gravitational potential energy of particle P at a general point of its motion?
What is the kinetic energy of particle P at a general point of its motion?
What is the potential energy stored in each spring at a general point of its motion?
How would I write an equation representing the total mechanical energy for the system at a general point of its motion?

You can assume that air resistance and other frictional forces can be ignored in this question
See attachment
a) Define a datum for the gravitational potential energy of particle P.
b) Write down the gravitational potential energy of particle P at a general point of motion.
c) Write down the kinetic energy of a particl

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.20 N is applied. A 1.200 kg particle rests on a friction-less horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t=0.

A small particle slides along a frictionless wire. If the particle's speed at point A is 8.85m/sec how fast is it moving at point B if it must go up a 2m incline?

A 1.50 box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.00 , and then is released from rest.
By how much will the box compress the weaker spring?
What is the max

Prove that the De Broglie wavelength associated with a particle having kinetic energy K which is not negligible compared to its rest energy m_0 c^2 is given by
lemda = [h/(m_0 K)^(1/2)](1 + K/2m_0 c^2)^(-1/2)
The complete solution is in the attached file.

An 80kg man jumps from a height of 2.5m onto a platform mounted on springs. The spring compress 0.240 below its initial position and then it rebounds. Platform & spring have negligible mass.
a) What is the spring's force constant?
b) What is his speed when the spring is compressed 0.120m?
c) If he gently steps on the plat

Please see the attached file.
1.
A particle of mass m moves in one dimension in an infinite square well. Suppose that at time t=0 its wave function is
Psi(x,0) = A[(L/2)^2-x^2]
a. Find the probability of obtaining value En of the particleenergy where En is one of the energy eigenvalues
b. Determine the expectation v

A particle of mass m is confined to move in a narrow, straight tube of length a which is sealed at both ends with V=0 inside the tube. Treat the tube as a one-dimensional infinite square well. The tube is placed at an angle theta relative to the surface of the earth. The particle experiences the usual gravitational potential V=

See attached file for full problem description.
7.8 Consider a region of space divided by a plane. The potential energy of a particle in region 01 is U1 and in region 02 it is U2.
If a particle of mass m and with speed v1 in region 01 passes from region 01 to region 02 such that its path in region 01 makes an angle theta1