Question for anyone who can help me please

[jen043081]

A weight hanging on a vertical spring is set in motion with a downward velocity of 6 cm/sec from its equilibrium position. Assume that the constant w for this particular spring and weight combination is 2. Write the formula that gives the location of the weight in centimeters as a function of the time t in seconds. Find the amplitude and period of the function and sketch its graph for t in the interval [0,2(pie)][/i][/b][/tex][/list][/code]

 

[Doc Al]

Simple Harmonic Motion

What have you done and where did you get stuck?

 

[M98Ranger]

The formula that gives the location of the weight in centimeters as a function of time t is:
x(t) = A*cos(wt) + h
where A is the amplitude, w is the angular frequency (in radians per second), and h is the initial position of the weight.

In this case, we know that the initial velocity is 6 cm/sec downwards, so h = 6. And we are given that the constant w = 2.

Therefore, the formula becomes:
x(t) = A*cos(2t) + 6

To find the amplitude, we can use the fact that the amplitude is the maximum displacement from the equilibrium position. In this case, since the weight is set in motion with a downward velocity, the amplitude will be the distance from the equilibrium position to the lowest point of the weight's motion. This distance is 6 cm, so the amplitude A = 6.

To find the period, we can use the formula T = 2(pi)/w. In this case, T = 2(pi)/2 = pi seconds.

Sketching the graph, we can see that the weight will oscillate between a maximum displacement of 6 cm downwards and a minimum displacement of 6 cm upwards, with a period of pi seconds. The graph will be a sinusoidal curve, starting at the equilibrium position and moving downwards.

I hope this helps!