The energy stored in a capacitor is given by:

where
U is the energy
C is the capacitance
V is the potential difference
The capacitor in this problem has capacitance

So if we re-arrange the previous equation, we can calculate the potential V that should be applied to the capacitor to store U=1.0 J of energy on it:
The momentum p of a moving particle is the product between its mass, m, and tis velocity, v:

In our problem, we know

and

, and using the relationship mentioned above, we can find the mass m of the particle:
To solve this problem it is necessary to apply the concepts related to frequency as a function of speed and wavelength as well as the kinematic equations of simple harmonic motion
From the definition we know that the frequency can be expressed as

Where,


Therefore the frequency would be given as


The frequency is directly proportional to the angular velocity therefore



Now the maximum speed from the simple harmonic movement is given by

Where
A = Amplitude
Then replacing,


Therefore the maximum speed of a point on the string is 3.59m/s