`y = 2sin(5x)` Find the period and the amplitude
This would be an example of what's called a sinusoidal function. The general form for that is:
y = A*sin(Bt-C)+D
Where A --> amplitude
B --> period = 2*pi/B
C --> phase shift = C/B
D --> vertical shift
So, simply matching the numbers up, the amplitude would be 2. And, the period would be 2*pi/5 = 0.4*pi.
As this question has been posted in the Maths section, I am assuming that it is not related to Simple Harmonic Motion.
If a function f(x) has a period = t, then the function n*f(kx) has a period = t/k
We know that the function f(x) = sin(x) has a period = 2*pi. Thus the function f(x) = 2sin(5x) will have a period = (2/5)*pi.
The maximum value of sin(5x) is 1 and the mean value is 0. Thus the amplitude of y=2sin(5x) is equal to 2.
Refer to the graph attached for better understanding.