Answer:
Explained
Explanation:
A) The total energy of the system is defined by the energy at maximum amplitude, which we'll call A. At that point, the energy of the system is
E = 1/2×m×A^2;
since energy is conserved, this is also the total amount of energy that the system ever has.
So at x=1/2A,
the potential energy of the system is 1/8×m×A^2
which is one-fourth of the system's total energy. Therefore, the remaining three-fourths is kinetic.
B) (i) Doubling the maximum amplitude will quadruple the total energy:
(ii) Doubling the maximum amplitude will double the maximum velocity
(iii) Doubling the maximum amplitude will double the maximum acceleration: m×a = -k(2A)
(iv) Doubling the maximum amplitude leaves the period unchanged:
(neither m nor k has changed).