Why this and <z>0 is zero in three dimensional oscillator?

A magnesium atom (mass ≈≈ 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 1014 Hz. What is the effective spring constant of the forces holding the atom in the crystal?

b) If a mass mis placed at the end of a spring, and if the mass is pulled downward and released, the mass-spring system will begin to oscillate. The displacement y of the mass from its resting position is given by a function of the form y = c,cos wt + c, sin wt (1) where w is a constant that depends on spring and mass. Show that set of al functions in (1) is a vector space.

amass 1 =0.3Kg related with horizontalsp oscilltes with srig constant 30 g /s AL £=05ec the mass it X (1) = it veloity () =2 /566 in @ gl frequency o) period. © freauency. {d) amplitude A and initial phasc. (6 maimum veloity and maxismum acclertion, () total energy., (@ poieiiaenesgy and Kineic energy at he posiion = 1) =413

Problem 2: A 0.55-kg mass oscillates according to the equation x(t)=0.69 cos(9.5t), where the position x(t) is measured in meters. Part (a) What is the period, in seconds, of this mass? T= sin() cos() tan() 9 HOME cotan() asin() acos() E 4 5 atan() acotan() sinh() * 1| 2 3 +| - vol BACKSPACE DEL CLEAR cosh() tanh() cotanh() END ODegrees O Radians Submit Hint Feedback I give up! Part (b) At what point during the cycle is the mass moving at it's maximum speed? Part (c) What is the maximum acceleration of the mass, in meters per square second? Part (d) At what point in the cycle will it reach it's maximum acceleration?

(a) An oscillating object repeats its motion every 3.3 seconds. (i) What is the period of this oscillation? (ii) What is its frequency? (iii) What is its phase rate (i.e. angular frequency)? (b) A magnesium atom (mass of 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 10l3 Hz. What is the effective spring constant of the forces holding that atom in the crystal? (c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what would be the person's period of oscillation T? (You should not need the person's mass, but if you think you do, assume and state a value.) (ii) Find T for Az = 45 cm. Check: For Az = 20 cm you should find T = 0.90 s.

Which of the following relations between the group and phase velocities is false? (a) vg = v – 1 dv dv (b) v, = v + k- dk k dn (c) vg n dk C (d) Vg = dn n+ w do up (e) vg = = 1V dk a 9.

A block of mass m is attached to a spring with force constant, k and oscillate at a frequency f. If the mass is changed to m′ = m/2, and the spring force is changed to k’= 2k, then the new frequency f’of the oscillation would be?

3:25 1 Search A long string attached to a mass M forms a simple pendulum. The string, however, is weak enough so that it is likely to break at some point in the oscillation if you let it swing. You pull the mass back and start it oscillating. ack the сar ad? v 70 q At what point in the cycle is the string most likely to break? at a 1. Just after release. 2. Just when the mass passes through the point where the string is vertical. 3. Just after the mass turns around to re- turn. 4. Just after the mass returns to the starting point. inting 5. It is equally likely to break at all posi- tions.