Answer:
a) w = 1.08 rad / s
, b) θ = π / 12 cos (1.08 t - 1,296)
, c) w = - 0.2827 sin (1.08t - 1,296)
, d) energy decrease
Explanation:
a) The oscillatory movement of a simple pendulum has the angular velocity
w = √(L / g)
w = √(0.35 / 0.300)
w = 1.08 rad / s
b) it is requested to find the equation of angular displacement
θ = θ₀ cos (wt + φ)
We replace
θ = π / 12 cos (1.08 t + φ)
To find the constant let's use the value they give
θ = θ₀ for t = 1.2 s
θ = θ₀ cos 1.08 1.2 + φ)
Cos (1,296 + φ) = 1
1,296 + φ = cos⁻¹ 1
Remember that the angles must be in radians
φ = 0 - 1,296
The final equation is
θ = π / 12 cos (1.08 t - 1,296)
c) the angular velocity is
w = dθ / dt
w = π / 12 (- 1.08 sin (1.08t - 1,296))
w = - 0.2827 sin (1.08t - 1,296)
d) if addamping force is included, part of the energy dissipates, therefore the total energy must decrease
e) The period of a physical pendulum is
w = √ (mg d / I)
Where I is the moment of inertia that is of the form
I = cte m R²
w = √ (m g d / cte md2) = √ (g / d) √(1/cte)
Simple pendulum wo = √ (g / d)
w = w₀ 1/√cont
As we see the angular velocity of this pendulum change due to the constant that accompanies the moment of inertia. In general this constant is less than by which the angular velocity the angular velocity increases
