the plank when the amplitude of oscillation of the plank becomes

less than T = 1.0 s.

4.33. Find the time dependence of the angle of deviation of a

mathematical pendulum 80 cm in length if at the initial moment the

pendulum

(a) was deviated through the angle 3.0° and then set free without

push;

(b) was in the equilibrium position and its lower end was imparted

the horizontal velocity 0.22 m/s;

(c) was deviated through the angle 3.0° and its lower end was im-

parted the velocity 0.22 m/s directed toward the equilibrium position.

4.34. A body A of mass m 1 = 1.00 kg and a body B of mass m 2 =

4.10 kg are interconnected by a spring as shown in Fig. 4.9. The

body A performs free vertical harmonic oscilla-

tions with amplitude a = 1.6 cm and frequency

= 25 s-1. Neglecting the mass of the spring,

find the maximum and minimum values of force

that this system exerts on the bearing surface.

4.35. A plank with a body of mass m placed

on it starts moving straight up according to

the law y = a (1 — cos cot), where y is the

displacement from the initial position, co = (^) Fig. 4.9.

= =- 11 s-1. Find:

(a) the time dependence of the force that the body exerts on the

plank if a = 4.0 cm; plot this dependence;

(b) the minimum amplitude of oscillation of the plank at which

the body starts falling behind the plank;

(c) the amplitude of oscillation of the plank at which the body

springs up to a height h = 50 cm relative to the initial position (at

the moment t = 0).

4.36. A body of mass in was suspended by a non-stretched spring,

and then set free without push. The stiffness of the spring is x.

Neglecting the mass of the spring, find:

(a) the law of motion y (t) , where y is the displacement of the body

from the equilibrium position;

(b) the maximum and minimum tensions of the spring in the pro-

cess of motion.

4.37. A particle of mass in moves due to the force F = — amr,

where a is a positive constant, r is the radius vector of the particle

relative to the origin of coordinates. Find the trajectory of its motion

if at the initial moment r = roi and the velocity v = voj, where i

and j are the unit vectors of the x and y axes.

4.38. A body of mass m is suspended from a spring fixed to the

ceiling of an elevator car. The stiffness of the spring is x. At the mo-

ment t = 0 the car starts going up with an acceleration w. Neglecting

the mass of the spring, find the law of motion y (t) of the body rela-

tive to the elevator car if y (0) = 0 and y (0) = 0. Consider the fol-

lowing two cases: