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CAN SOMEONE EXPLAIN ME THE GIVEN FORMULA IN PHYSICS IN ABOUT 50 TO 100 WORDS AND CAN GIVE ME SOME EXAMPLES BASED ON IT
NOTE:DON'T GIVE ANSWERS WHICH MAKE NO SENSE OR ELSE I WILL REPORT
Answers
Simple Pendulum
It is a arrangement of a heavy point mass suspended by a weightless, inextensible and perfectly flexible spring from a rigid support about which it is free to oscillate.
Restoring torque = - mg sin∅l
τ = - mgl sin∅
∅ → 0, sin∅ ≈ ∅
∴ τ = -(mgl)∅
As τ = - k∅
∴ k = mgl ............(1st equation)
Also, Inertial factor 'I' = ml²
T = 2π √[(Inertial factor)/(Spring factor)]
T = 2π √[(ml²)/(mgl)
T = 2π √(l/g)
Examples:
1) If we take a Simple Pendulum to mountain will it's time period increases or decreases?
→ Value of g decreases. So, time period increases. As,
T = 2π √(l/g)
2) What is the period of a simple pendulum with a length of 2 m?
→ T = 2π √(l/g)
T = 2 × 3.14 √(2/10)
T = 2.81 s
Additional Information
Expression for Time period:
For a particular executing SHM
A = -ω²y
∴ F = mA = - mω²y .........(1st equation)
Also, F = -ky ...........(2nd equation)
On comparing (1st equation) and (2nd equation) we get,
→ -ky = -mω²y
→ ω² = k/m
→ ω = √(k/m)
→ 2π/T = √(k/m)
→ T = 2π √(m/k)
Therefore,
T = 2π √[(Inertial factor)/(Spring factor)]
