In the diagram below, if y = 4 m, x = 3 m, and θ = 30 degrees, calculate the value of F for which the body is in equilibrium.*1 point

Find the equilibrium point, the maximum and the minimum values for the the following trigonometric function. Sketch the graph in your notebook.𝑓(𝑥)=4cos(4𝑥)+4

Write the necessary equations of equilibrium of the object shown in the figure below. Take the origin of the torque equation about an axis perpendicular to the page through the point O. (Let counterclockwise torque be positive and let forces to the right and up be positive. Use the following as necessary: the forces Rx, Ry, Fx, Fy, and Fg; the length ℓ of the object; and the angle 𝜃 that the object makes with the horizontal.)A rod of length ℓ makes an acute angle 𝜃 clockwise from the horizontal. A point at the left end of the rod is labeled O. Five forces act on the rod as follows.A force with magnitude Rx begins at the left end of the rod and points horizontally left.A force with magnitude Ry begins at the left end of the rod and points vertically up.A force vector Fg begins at the center of the rod and points vertically down.A force with magnitude Fx begins at the right end of the rod and points horizontally right.A force with magnitude Fy begins at the right end of the rod and points vertically up.ΣFx = = 0ΣFy = = 0Σ𝜏 = 0 = 0

f sin cos3 0θ θ− = and ,0 90º º< <θ find the value of .θ

A man raises a joist (length = l) by pulling a rope attached to point B. The centre of mass is located at the centre of the beam and the system is at equilibrium.Variable l αβValue 5 40 25Units [m] [degrees] [degrees]Hints: The reaction does not necessarily act along the joist. This question can be solved without the use of simultaneous equations (Use 3 Force Bodies).Given the information in the table above, determine:1) the angle of the resultant reaction, θ, at point A if at that point the ledge acts as a rough surface.

A simple pendulum consists of a ball of mass 3kg suspended from the ceiling using a string of length 4 meters. The ball is displaced from its equilibrium position by a small angle of 5°. a) What is the magnitude of the restoring force that moves the ball toward its equilibrium position and produces simple harmonic motion?