An object oscillating in simple harmonic motion

[lorenz0]

Homework Statement

An object oscillates in simple harmonic motion, reaching a maximum velocity of $1.2m/s$ whenever it passes through the central position, which occurs every $3.6s$.
Find the amplitude and maximum acceleration of the harmonic motion.

Relevant Equations

$v_{max}=\omega A$, $a_{max}=\omega^2 A$, $\omega=\frac{2\pi}{T}$

Since it passes through the origin every $3.6s$ the period is $T=3.6s$ hence $\omega=\frac{2\pi}{\omega}=\frac{2\pi}{3.6}\frac{rad}{s}$ thus $A=\frac{v_{max}}{\omega}=\frac{1.2}{\frac{2\pi}{3.6}}m\simeq 0.69m$ and $a_{max}=\omega^2 A=(\frac{2\pi}{T})^2 A=(\frac{2\pi}{3.6})^2 \cdot 0.69\simeq 2.1\frac{m}{s^2}$.

What I have done makes sense to me so I don't understand why the solutions to this problem state that $A=2.8m$ and $a_{max}=0.52\frac{m}{s^2}$. Comment are welcome, thanks.

 

[PeroK]

Since it passes through the origin every $3.6s$ the period is $T=3.6s$

It passes through the origin twice per period!

 

[gneill]

Start with a sketch of a generic SHM and label the times of the zero-crossings:

 

[PeroK]

What I have done makes sense to me so I don't understand why the solutions to this problem state that $A=2.8m$ and $a_{max}=0.52\frac{m}{s^2}$. Comment are welcome, thanks.

These don't look right to me. Especially the acceleration, which looks very low.

 

[PeroK]

What I have done makes sense to me so I don't understand why the solutions to this problem state that $A=2.8m$ and $a_{max}=0.52\frac{m}{s^2}$. Comment are welcome, thanks.

To get those answers you need the period to be $14.4s$.

 

[lorenz0]

It passes through the origin twice per period!

Ah, I understand my mistake now, thanks!

 

[Herman Trivilino]

Homework Statement:: An object oscillates in simple harmonic motion, reaching a maximum velocity of $1.2m/s$ whenever it passes through the central position, which occurs every $3.6s$.

That's a poorly worded statement. The oscillator will pass through the central position twice per period, but will have a maximum velocity only once per period. The statement can be fixed by specifying that it reaches a maximum speed of 1.2 m/s whenever it passes through the central position.