Answer:
No, the pendulum's period of oscillation does not depend on initial angular displacement.
Explanation:
Given that,
For small angle, the pendulum's period of oscillation depend on initial angular displacement from equilibrium.
We know that,
The time period of pendulum is defined as
Where, l = length of pendulum
g = acceleration due to gravity
So, The time period of pendulum depends on the length of pendulum and acceleration due to gravity.
It does not depend on the initial angular displacement.
Hence, No, the pendulum's period of oscillation does not depend on initial angular displacement.
Answer:
During <u>winter (late December/early January)</u> the Earth is closest to the Sun and during <u>summer (late June/early July)</u> the Earth is farthest from the Sun.
Explanation:
In the northern hemisphere, the earth usually comes closer to the sun during the time of winter season, mostly in late December or early January.
On the other hand, the earth is farthest from the sun during the time of summer season, mostly in late June or early July.
When the earth is closer to the sun, during the winter, it is comparatively cold. It is due to the absorption of a lesser amount of incoming solar radiation. The tilt of the earth is also responsible for this low temperature.
But, when the earth is farthest from the sun, during the summer, it is comparatively hot. It is due to the absorption of a large amount of incoming solar radiation.
Answer:
0.832 m/s
Explanation:
The work done by the spring W equals the kinetic energy of the object K
The work done by the spring W = 1/2k(x₀² - x₁²) where k = spring constant, x₀ = initial compression = 0.065 m and x₁ = final compression = 0.032 m
The kinetic energy of the object, K = 1/2mv² where m = mass of object and v = speed of object
Since W = K,
1/2k(x₀² - x₁²) = 1/2mv²
k(x₀² - x₁²) = mv²
mv² = k(x₀² - x₁²)
v² = [(k/m)(x₀² - x₁²)]
taking square root of both sides, we have
v = √[(k/m)(x₀² - x₁²)] since ω = angular frequency = √(k/m),
v = √[(k/m)√(x₀² - x₁²)]
v = ω√(x₀² - x₁²)]
Since ω = 14.7 rad/s, we substitute the other variables into the equation, so we have
v = 14.7 rad/s × √((0.065 m)² - (0.032 m)²)]
v = 14.7 rad/s × √(0.004225 m² - 0.001024 m²)]
v = 14.7 rad/s × √(0.003201 m²)
v = 14.7 rad/s × 0.056577
v = 0.832 m/s
