Đáp án:
a) 100 N/m; 0,5 J
b) 0,1 s; 10 Hz
c) ±5 cm; ±50√30 cm/s.
Giải thích các bước giải:
a) $k=mω^2=0,1.(10π)^2=100 \ (N/m)$
`W=\frac{1}{2}kA^2=\frac{1}{2}.100.0,1^2=0,5 \ (J)`
b) $ω'=2ω=2.10π=20π \ (rad/s)$
⇒ $T'=\dfrac{2π}{ω'}=\dfrac{2π}{20π}=0,1 \ (s)$
⇒ $f'=\dfrac{1}{T'}=\dfrac{1}{0,1}=10 \ (Hz)$
c) `W_d=3W_t ⇔ W-W_t=3W_t ⇔ W=4W_t`
⇔ `\frac{1}{2}kA^2=4.\frac{1}{2}kx^2`
⇔ `A^2=4x^2 ⇔ A=2|x| ⇔ x=±A/2=±5 \ (cm)`
`W_d=W-W_t=\frac{1}{2}k(A^2-x^2)=\frac{1}{2}mv^2`
⇔ `k(A^2-x^2)=mv^2`
⇔ $v=±\sqrt{\dfrac{k(A^2-x^2)}{m}}=±\sqrt{\dfrac{100.(0,1^2-0,05^2)}{0,1}}=±\dfrac{\sqrt{30}}{2} \ (m)=±50\sqrt{30} \ cm/s$