Answer:
a_max = 50 cm/s^2
Explanation:
To find the magnitude of the maximum acceleration of the particle, you take into account the equation of motion in a simple harmonic motion:
[tex]x=Acos(\omega t)[/tex]
ω: angular velocity = 10 rad/s
A: amplitude = 5 cm
The acceleration is given by:
[tex]a=\omega^2 x[/tex]
and the maximum acceleration is obtained when the cosine function is maximum, that is, when cos(wt) = 1. Then, you have:
[tex]a_{max}=\omega^2 x_{max}=\omega^2A[/tex]
Then, you replace the values of w and A in order to calculate a_max:
[tex]a_{max}=(10rad/s)^2(5cm)=50\frac{cm}{s^2}[/tex]
hence, the maximum acceleration is 50 cm/s^2
