Consider classical and quantum harmonic oscillators. When the classical harmonic oscillator is in the ground state, i. e., at rest, it sits still at the equilibrium position. This would correspond to the limit of the oscillatory solutions with po = 0 and Xo = 0, for which the total energy E is zero. The corresponding case for the quantum harmonic oscillator would have the expectation values of momentum and position zero as well:
= 0

The position of a crate sliding down a ramp is given by x=(0.05t^3) m, y=(1.7t^2) m, z=(6−0.85t^5/2) m, where t is in seconds. (a) determine the magnitude of the crate's velocity when t = 2 s. (b) determine the magnitude of the crate's acceleration when t = 2 s.

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.

Avehicle accelerates from 0 to 30 m/s in 10 seconds on a straight road