A skydiver of mass 50 kg falls vertically downward from an

Question

1. Add the following three SHMs to obtain a resultant SHM in the form  x(t)=Asin(ωt+Φ);
x1(t) = -3.17sin(ωt+5.08)
x2(t) = +4.67sin(ωt+1.78)
x3(t) = +2.50cos(ωt-2.00)

Also, draw a reasonably accurate phasor diagram for this situation.

2. A block of mass in sits atop a platform of mass M which is attached to a spring of force constant K. The lower end of the spring is anchored to the floor. At the instant shown, the system is in static equilibrium. Now the spring is extended vertically upward by distance Δy and the masses are released at rest. What is the maximum value of Δy such that the mass m will remain in contact with the platform as time proceeds?

3. A skydiver of mass 50 kg falls vertically downward from an initial state of rest at t=0. Two forces act on the skydiver, her weight, and a drag force proportional to her velocity. The drag constant is b=9.00 Ns/m.

(a) Find the terminal velocity of the skydiver.

(b) Find the time elapsed and the distance fallen when the skydiver has achieved 80% of her terminal velocity.

(c) If, at the time found in part (b), the skydiver suddenly spreads her aims and legs and increases the drag constant by a factor of 2, describe the subsequent motion (i.e., solve for vy as a function of t). Plot a graph of the skydiver's velocity versus time from t=0 to twice the elapsed time computed in (b).

4. A particle of mass m moves in a potential well whose potential energy function is given by

PE(x) = E₀ coshax= E₀((e^-ax + e^-ax)/2)
Find the equilibrium position, effective spring constant, and angular frequency of small oscillations about the equilibrium position for this particle.

Answer 1

These few questions are based on a reasonably accurate phasor diagram for 1. Add the subsequent three SHMs to attain a consequential SHM in the form x(t)=Asin(?t+F); x1(t) = -3.17sin(?t+5.08) x2(t) = +4.67sin(?t+1.78) x3(t) = +2.50cos(?t-2.00) As well, draw a reasonably precise phasor diagram for this situation. 2. A block of mass in sits atop a platform of mass M that is attached to a spring of forces constant K. The lesser end of the spring is anchored to the floor. At the instant revealed, the system is in static equilibrium. Now the spring is expanded vertically upward via distance ?y and the masses are liberated at rest. What is the maximum value of ?y these that the mass m will remain in contact through the platform as time proceeds?