Answer:
(a) 45 cm (b) 3.305 rad/sec (c) 1.4875 m/sec
Explanation:
It is given that the motion is simple harmonic and it takes 1.90 sec to complete a cycle
The frequency is defined as the reciprocal of time taken to complete one cycle so
(a) As it is given that the height of each bounce above the equilibrium positon is 45 cm so amplitude will be 45 cm
(b) The angular frequency ω is given by rad/sec
(c) The maximum speed is given by
where ω is angular frequency of the motion and A is the amplitude So
Answer:
A) K / K₀ = 4 b) v / v₀ = 4
Explanation:
A) For this exercise we can use the conservation of mechanical energy
in the problem it indicates that the displacement was doubled (x = 2xo)
starting point. At the position of maximum displacement
Em₀ = Ke = ½ k (2x₀)²
final point. In the equilibrium position
= K = ½ m v²
Em₀ = Em_{f}
½ k 4 x₀² = K
(½ K x₀²) = K₀
K = 4 K₀
K / K₀ = 4
B) the speed value
½ k 4 x₀² = ½ m v²
v = 4 (k / m) x₀
if we call
v₀ = k / m x₀
v = 4 v₀
v / v₀ = 4