A simple pendulum can be described by the equation d2 ?(t) / dt2 = -(g/l)?(t) wh

Question

A simple pendulum can be described by the equation
d2 ?(t) / dt2 = -(g/l)?(t)

where ? is the angular displacement from the vertical, l is the length of the pendulum and g = 9.81 m s-2

2) Consider a simple pendulum, call it pendulum 1, with length 0.30 m that is released from rest at ? = 0.10 rad at t = 0.00 s. Write down the equations thatexpress the angular displacement ?, and angular velocity d?/ dt, of thependulum as functions of time, taking care to determine the values of anyconstants you introduce. The phrase ‘released from rest’ implies that d?/ dt = 0 at the moment of release.

Explanation / Answer

For a simple pendulum the time period is given by
T = 2pi(l/g)^1/2
where l is length of pendulum and g is acceleration due to gravity and has value g = 9.8 m/s^2
let the angular displacement of pendulum be A
we know that
S = l * A
S is length of arc
differentiating the above equation we get
dS/dt = l * dA/dt
or v = l * w
where w is angular velocity of pendulum
the speed of pendulum is
v = A * w * sin(wt)
when wt = 90o then
v_max = A * w

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.