السلام عليكم و رحمة الله و بركاته،،

أرجو أن تحلوا الأسئلة التالية جميعا، بالإضافة إلى سؤال المشاركة الذي طرحته عليكم اليوم.

Q23.

A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:?? (compared to T)

Q28.

A 3 kg block, attached to a spring, executes simple harmonic motion with a displacement given by where x is in meters and t is in seconds. The spring constant of the spring is:??

Question:

A mass-spring system (m = 100 grams, k = 10 N/m), as in the figure below, is extended by 4 cm, and given a blow (ضربة), at time t = 0 s, to the left such that it speed is m/s. The displacement as a function of time is described as: x(t) = A sin(wt + d).

Find A, w and d?

Interaction:

In class, we said that the homogeneous 2^nd order linear differential equation with constant coefficients: d²x/dt² + w² x = 0

Has a solution of the form: x(t) = A sin(wt + d).

We said, this can also be written as: x(t) = a sin(wt) + b cos(wt).

It can also be written as: x(t) = a e^iwt + b e^-iwt_.

i- Find the relationship between {A,d}and {a,b}, and

ii- Find the relationship between {a,b}and {a,b}.

أرجو لكم المتعة و السرور، و السلام عليكم و رحمة الله و بركاته،،

د. زين بن حسن يماني

محاضر دورة الاهتزازات و الموجات