As we know that KE and PE is same at a given position
so we will have as a function of position given as

also the PE is given as function of position as

now it is given that
KE = PE
now we will have




so the position is 0.707 times of amplitude when KE and PE will be same
Part b)
KE of SHO at x = A/3
we can use the formula

now to find the fraction of kinetic energy



now since total energy is sum of KE and PE
so fraction of PE at the same position will be


The energy bar eaten by Sheila has chemical energy locked up inside it. This chemical energy is converted to mechanical energy in form of potential and kinetic energy and this in turn is converted to heat energy as the run progresses. Thus, the energy changes are: chemical energy to mechanical energy [kinetic and potential] and finally to heat energy.
Answer:
The Total Mechanical Energy
As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy.
Explanation:
Velocity = 14 m/s
Time = 20 s
Displacement = Velocity×Time = (14×20) m = 280 m
The displacement is 280 m towards the direction of motion.