The Angular Displacement $\theta$ Of a Simple Pendulum Is Given By $\theta = \theta _ { 0 } \sin ( \omega t + \phi )$

question 153

Essay

The angular displacement $\theta$ of a simple pendulum is given by $\theta = \theta _ { 0 } \sin ( \omega t + \phi )$ where $\theta _ { 0 }$ is the angular amplitude, $\omega$ the angular frequency and $\theta$ a phase constant depending on initial conditions. If we are given that $\omega$ = 10 and $\phi = \frac { \pi } { 2 }$
, find the angular velocity $\frac { d \theta } { d t }$ when $\theta = \frac { \theta _ { 0 } } { 2 }$ .

---

Definitions:

Maintenance Agreement

A contractual agreement where one party agrees to maintain assets owned by another party, often including repairs and replacements.

Financing Profit

The profit generated from the difference between the cost of financing sources (such as loans) and the income generated from their use.

Inventory Cost

The total cost associated with obtaining, storing, and managing inventory, including purchase costs, storage costs, and any other expenses related to maintaining or handling inventory.

Leased Lathe

A contract arrangement where a lathe, a machine tool used for shaping metal or wood, is rented for use over a specific time period.