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?

Question 2 a) A laminar boundary layer profile may be assumed to be approximately of the form u/Ue= f (n)=f(y/8) i) Use an integral analysis with the following two-segment velocity profile, ƒ (n)=(n/6)(10–3n−1³), for 0≤7≤0.293 and ƒ (7) = sin (л7/2) for 0.293≤n≤1, to find expressions for the displacement thickness &*, the momentum thickness e, the shape factor H, the skin-friction coefficient c, and the drag coefficient CD. ii) Derive an expression for the velocity normal to the stream wise direction given that, u/U₂ = f(n). iii) Hence obtain the velocity normal to the stream wise direction for the above two- segment velocity profile.

(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.

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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

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.

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What is the magnitude of Å + B + Č, where A = 1.00 i + 4.00 j - 1.00 k, B = 3.00 i - 1.00 j - 4,00 k and Č = -1.00 i + 1.00 j? A) 2.00 B) 6.78 C) 7.07 D) 8.12 E) 10.76

If you were examining a system in which a spring was oscillating, how would the period of vibrations be changed if the Gravitational Acceleration were decreased by 5%? O The period is unaffected O The period becomes 2pi O The period is shorter O The period is longer