Answer: Period = 0.2 seconds; frequency = 5Hz
Explanation:
Number of oscillations = 50
Time required = 10 seconds
Period (T) = ?
Frequency of the oscillations (F) = ?
A) Recall that frequency is the number of oscillations that the mass spring system completes in one second.
i.e Frequency = (Number of oscillations / time taken)
F = 50/10 = 5Hz
B) Period, T is inversely proportional to frequency. i.e Period = 1/Frequency
T = 1/5Hz
T = 0.2 seconds
Thus, the the period and frequency of the oscillations are 0.2 seconds and 5Hz respectively.
Answer:
D(t) = 8(0.83)^(t) cos 38πt
Explanation:
We are told that the spring oscillates 19 times each second.
Thus, period = 1/19
We are also told that it's pulled 8cm downwards and the amplitude decreases by 17% each second.
Thus;
Amplitude;A = 8 × (1 - (17/100))^(t)
A = 8(0.83)^(t)
If we consider the function;
y = A cos (bx - c) + d
Now, 2π/b = period
So, 1/19 = 2π/b
b = 38π
So, D(t) = 8(0.83)^(t) cos (38πt - c) + d
Since we started from minimum,
Vertical shift, d = 0 and horizontal shift c = 0
So,we now have;
D(t) = 8(0.83)^(t) cos 38πt
Answer:
Length of the ramp, l = 31.22 feet
Explanation:
It is given that,
A doorway is 2.45 ft above the ground, AB = 2.45 ft
Angle between the ground and the ramp is, 
Applying trigonometry,
AC = 31.22 ft
So, the length of the ramp is 31.22 feet. Hence, this is the required solution.
