# Vibration Question: BoB Released from Rest, Solve for Theta & Vel/Acc at 1.6s

• FChebli
In summary, the problem involves a Bob released from rest with an L of 102 cm and an angle theta of +-5 degrees. The task is to determine the angle and magnitudes of velocity and acceleration after 1.6 seconds assuming simple harmonic motion. The equation for theta is given as theta = A sin (w t + phai), where A is the maximum value, omega is the frequency, and phi is the phase. The values of A and omega can be found from the given information, while phi can be found by setting t = 0.
FChebli

## Homework Statement

:[/B]

BoB released from rest, L = 102 cm, theta = +-5 degrees, g = 9.81 m/s2
assume a SHM
(I) Determine the angle theta after 1.6 s
(II) Determine the magnitudes of velocity & acceleration of the BoB at 1.6 s

## Homework Equations

theta = A sin (w t + phai)

## The Attempt at a Solution

Does phai represent the period? And how do I get it?
Do I derive theta once & twice? And why?
How do I get w & A?

Thank you!

Welcome to PF!

Hi FChebli! Welcome to PF!

(have a theta: θ and a phi: φ and an omega: ω )

θ = A sin(ωt + φ)

A is the maximum value (θ varies between ±A), which you can find from the question

ω is the frequency … to find the period, you need the value of t which makes (ωt + φ) increase by 2π

φ is the phase … it's often zero, but not always … you find it by putting t = 0, and seeing what θ is (or dθ/dt, if that's given instead)

Thank you so much! :)

## 1. What is the equation for calculating theta?

The equation for calculating theta is θ = θ0 + ω0t + ½αt2, where θ is the angle in radians, θ0 is the initial angle, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time in seconds.

## 2. How do you calculate velocity at a specific time?

To calculate velocity at a specific time, you can use the equation v = v0 + at, where v is the velocity at the specific time, v0 is the initial velocity, a is the acceleration, and t is the time in seconds.

## 3. What is the formula for calculating acceleration?

The formula for calculating acceleration is a = (v - v0) / t, where a is the acceleration, v is the final velocity, v0 is the initial velocity, and t is the time interval in seconds.

## 4. How can I find the initial velocity if only the final velocity and acceleration are given?

To find the initial velocity, you can use the equation v0 = v - at, where v0 is the initial velocity, v is the final velocity, a is the acceleration, and t is the time interval in seconds.

## 5. Can I use the same equations for calculating theta, velocity, and acceleration for any object released from rest?

Yes, the equations for calculating theta, velocity, and acceleration can be used for any object released from rest, as long as the initial conditions (e.g. initial angle, initial velocity) and acceleration remain constant.

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