This is a mastering physics questions I’ve been trying to solve.
Since you have told that the graph is cosine function,
v = ωA cos (ωt + φ)
The maximum velocity is 10cm/s => ωA = 10 cm/s.
At time t = 0 its velocity is 5cm/s
5 = ωA cos φ = 10 cos φ
φ = 60° or π/3 radian
From the graph find another value for the velocity and its exact time t.
Substitute the value of v and t in the equation
v = 10 cos (ωt + π/3)
Since in the above equation v and t are known, you can solve the equation to find ω
Once you find ω you can find A from ωA = 10 cm/s.
Note ω= 2 pi f.
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What are the units. The amplitude of your graph is 10cm/s if the answer has units of m or something you’ll need to convert. It doesn’t matter that it’s a velocity amplitude, you have a graph showing velocity and 10 is the amplitude of your graph.
If they want the position amplitude you have to do something different. If you know calculus then you can take Acoswt derive it to get -Awsinwt so velocity amplitude is Aw while position amplitude is A. If you don’t know calculus hopefully they just told you that?
10/w where w is the angular frequency which is 2*pi*f
if you calculated frequency correctly then the position amplitude will be 10/pi cm