1. The height of a moving object is given by h(t) = e^(-0.3t) sin(5t) where h is
ID: 2836812 • Letter: 1
Question
1. The height of a moving object is given by h(t) = e^(-0.3t) sin(5t) where h is in cm and t is in seconds.
a) Find the first instant in time,t > 0,when the velocity is 0.
b) Find the first instant in time,t > 0,when the rate of change of velocity is 0.
2. A population of rabbits grows according to the logistic model P(t) =(1000e^0.12t)/(19 + e^0.12t) where P is in rabbits and t is in months.
a) What is the largest possible rate of change of P?
b) At what instant in time does this rate occur?
3. The function below is an example of a damped oscillator. Such functions appear in many physical settings.
f(t) = e^kt sin(bt) It is common for them to occur with unknown constants, which can be solved for if there is enough data. Give exact numerical answers. Units are not required.
a) Suppose that f'(0) = 2.Find b.
b) Suppose tha tf''(0) = -1.4.Find k.
4. The electric potential in a circuit is given by V(t) = A^ekt sin(bt) where A, k and b are constants.
a) ComputeV''(0).Your answer will include all of the constants.
b) Compute d2V/dt2 t = pi/(2b)
Explanation / Answer
Given that h(t) = e^(-0.3t) sin(5t)
V(t) = velocity at time t h
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