The angle made by the string of a simple pendulum with the vertical depends on time as θ = (π/90).sin[(π s⁻¹)t]. Find the length of the pendulum if g = π² m/s².
Answers
Given,
θ = (π/90).sin[(π s⁻¹)t]
Think it as little logical, you will find that it is very similar to x = ASinωt.
In place of x, there is θ, which shows angular displacement.
Comparing with this, value of angular velocity or angular frequency will be same for both.
Hence, ω = π
Now, we know that,
T = 2π/π
T = 2 seconds.
Hence, the time period of the pendulum is 2 seconds which means it is an seconds pendulum.
For length,
Using the formula,
where T is the time period, l is the length of the second pendulum and g is the acceleration due to gravity.
Note ⇒ g is not the real acceleration due to gravity but it is the g effective. Thu you can't assume its value to be 9.8. It varies with place and motion. Now, it is given in the question as π² m/s². Thus, we need to put this only.
2 = 2π√(l/π²)
4 = 4π² × l/π²
4 = 4 × l
l = 1 m.
Hence, the length of the second's pendulum is 1 m.
Hope it helps.
Answer:Given,
θ = (π/90).sin[(π s⁻¹)t]
Think it as little logical, you will find that it is very similar to x = ASinωt.
In place of x, there is θ, which shows angular displacement.
Comparing with this, value of angular velocity or angular frequency will be same for both.
Hence, ω = π
Now, we know that,
T = 2π/π
T = 2 seconds.
Hence, the time period of the pendulum is 2 seconds which means it is an seconds pendulum.
For length,
Using the formula,
where T is the time period, l is the length of the second pendulum and g is the acceleration due to gravity.
Note ⇒ g is not the real acceleration due to gravity but it is the g effective. Thu you can't assume its value to be 9.8. It varies with place and motion. Now, it is given in the question as π² m/s². Thus, we need to put this only.
2 = 2π√(l/π²)
4 = 4π² × l/π²
4 = 4 × l
l = 1 m.