Determine Speed & Acceleration of Spring Motion

In summary, the conversation discusses an object attached to a spring undergoing simple harmonic motion. The displacement x of the object as a function of time is given, along with the values of A and T. The conversation then moves on to calculating the speed and acceleration of the object at a certain time using the first and second derivatives of the displacement function. The speaker suggests doing research or consulting resources for further understanding.
  • #1
mikefitz
155
0
An 0.64-kg object is attached to one end of a spring, as in Fig. 10.14 and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing above. Please take the values of A and T as: A = 0.087 m and T = 1.8 s. With the aid of this data, determine


ive already calculated amplitude, angular frequency, spring constant.

I can't figure out how to calculate these:

(d) the speed of the object at t = 3.6 s

(e) and the magnitude of the object's acceleration at t = 3.6 s


any tips??
 
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  • #2
You have a function x(t) which represents displacement. Now, what do the first and second derivatives of this function with respect to time represent?
 
  • #3
sorry but I'm really lost here - can you please clarify what you mean by what the first and second derivatives with respect to time means? thanks for your patience
 
  • #4
mikefitz said:
sorry but I'm really lost here - can you please clarify what you mean by what the first and second derivatives with respect to time means? thanks for your patience

I don't want to sound uncooperative, but I think you should do some google-ing at this point or consult your physics/calculus books.
 

FAQ: Determine Speed & Acceleration of Spring Motion

What is the relationship between the mass of a spring and its speed and acceleration?

The mass of a spring does not directly affect its speed and acceleration, as these are determined by the force applied to the spring and the spring constant. However, a heavier mass may require a stronger force to achieve the same speed and acceleration as a lighter mass.

How do you calculate the speed of a spring in motion?

The speed of a spring in motion can be calculated by dividing the distance the spring travels by the time it takes to travel that distance. This is expressed by the formula v = d/t, where v is speed, d is distance, and t is time.

What factors can affect the acceleration of a spring?

The acceleration of a spring can be affected by the force applied to it, the spring constant, and any external factors such as friction or air resistance. The mass of the spring itself does not affect its acceleration.

How does the spring constant influence the speed and acceleration of a spring?

The spring constant, which is a measure of a spring's stiffness, affects the speed and acceleration of a spring by determining how much force is required to stretch or compress the spring. A higher spring constant means a greater force is needed for the same amount of stretch or compression, resulting in a greater speed and acceleration.

Can the speed and acceleration of a spring be measured without specialized equipment?

Yes, the speed and acceleration of a spring can be measured using basic equipment such as a ruler and a stopwatch. By measuring the distance traveled and the time it takes for the spring to travel that distance, the speed and acceleration can be calculated. However, more precise measurements can be obtained using specialized equipment such as motion sensors.

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