五、圖五電路中 R = 40 Ω，L = 5 mH，C = 2μF，開關 S 置於直流電壓源 vDC = 1V 很久後，於 t = 0 切換至交流電壓源 vAC = sinωt V， ω = 104 rad / sec，求出 t ≥ 0 之 vC (t)，須列出必要的分析數學式。（20 分）

一、英譯中：請將下面這段英文譯成正確、流暢的中文（30 分）The pervasive integration of smart surveillance in modern residential complexes has sparked a contentious debate over consumer privacy. While property managers advocate for heightened security, residents often object to the unconsented gathering of their biometric data. Under basic tort law, individuals possess a "reasonable expectation of privacy" in their domiciles, a right that technology constantly threatens to encroach upon. Users routinely click "agree" to lengthy terms of service, but this passive acquiescence does not necessarily constitute legally binding consent under scrutinized consumer protection frameworks. As regulatory bodies struggle to reconcile technological convenience with constitutional protections, consumers must remain vigilant, understanding that safeguarding digital privacy is no longer merely a personal preference, but a vital civil liberty.

五、圖五電路中 R = 40 Ω，L = 5 mH，C = 2μF，開關 S 置於直流電壓源 v_DC = 1V 很久後，於 t = 0 切換至交流電壓源 v_AC = sinωt V， ω = 10⁴ rad / sec，求出 t ≥ 0 之 v_C(t)，須列出必要的分析數學式。（20 分）

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