Finding Velocity and Acceleration in Simple Harmonic Motion

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To find the velocity and acceleration of a mass in simple harmonic motion described by the equation x = (0.2m) sin(3t), one must use calculus. The velocity is determined by taking the derivative of position with respect to time, dx/dt, while acceleration is found by taking the derivative of velocity with respect to time, dv/dt. By substituting the given position into these derivatives, expressions for both velocity and acceleration can be established. The discussion emphasizes the importance of combining these expressions with the position equation to solve for specific values. Understanding these steps is crucial for analyzing motion in simple harmonic systems.
vooov92
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Please help me,

Question
The equation of motion of a mass is given as x = (0.2m) sin (3t). Find the velocity and acceleration of the mass when the object is +5cm from its equilibrium position.
 
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Given position, how do you find velocity and acceleration? (What are the definitions of velocity and acceleration?)

Hint: Use a bit of calculus.
 
how??
for v i use dx/dt
for a i use dv/dt

so how to solve it, i also not understand the statement... anyone can help me
 
vooov92 said:
how??
for v i use dx/dt
for a i use dv/dt
Exactly. So find expressions for v and a. Then combine them with the expression for x.
 
Doc Al said:
Exactly. So find expressions for v and a. Then combine them with the expression for x.

can u show me the work step... can?
 
You were given an expression for x, so find dx/dt for that expression.
 
Last edited:
Redbelly98 said:
You were given an expression for x, so find dx/dt for that expression.

tq very much...
 
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